On Wednesday, the Iraqi Ministry of Defense claimed his No. 2 was killed in a coalition airstrike, a claim the U.S. military has not confirmed.
A U.S. official told CNN on Monday there is "no information" to indicate al-Baghdadi has been injured and, furthermore, there was recent intelligence indicating he "is a player" and is "absolutely participating" in the day-to-day running of ISIS.
The official said the United States had no information al-Baghdadi was at the location where the airstrike was said to have occurred in March.
Separately, Pentagon spokesman Col. Steven Warren said Monday the United States "has no reason to believe Abu Bakr Al Baghdadi has been injured in a coalition airstrike."
Then, on Thursday, ISIS released an online audio statement in which al-Baghdadi calls for recruits from around the world to "fight in his land or wherever that may be."
CNN Arabic speakers said the voice was consistent with al-Baghdadi's previous recordings and shows no signs of frailty.
Even so, the conflicting reports have spurred interest about other ISIS leaders who might emerge as al-Baghdadi's successor should he be incapacitated or die. ISIS has not publicly anointed a successor, but several senior figures could emerge as the next so-called "caliph."
Abu Alaa al-Afri
One of them, if he is still alive, is a shadowy operative called Abu Alaa al-Afri, who analysts believe would be expected to take control of the day-to-day running from al-Baghdadi if he was incapacitated. On Tuesday, the Iraqi Defense Ministry claimed a coalition air strike had killed him in Tal Afar in northern Iraq.
The Defense Ministry did not say when he was killed. A senior Iraqi security official who did not want to be named discussing sensitive intelligence told CNN the strike happened Tuesday.
Iraqi authorities have in the past been criticized for making inaccurate claims that ISIS leaders have been killed or injured.
U.S. Central Command said it had "no information to corroborate" that ISIS's second-in-command had been killed in a Coalition airstrike.
Hisham al-Hashimi, an adviser to the Iraqi government, said al-Afri is the deputy leader of ISIS and also goes by the name Abd al-Rahman Mustafa al-Qaduli -- a name that was added to the U.S. Rewards for Justice list just last week. The U.S. State Department offered a $7 million reward for information on him -- the highest for any ISIS leader apart from Abu Bakr al-Baghdadi, who is valued at $10 million.
According to the U.S. Treasury Department, which designated him as a "specially designated global terrorist" exactly a year ago, the man known as al-Qaduli was born in Mosul in either 1957 or 1959.
CNN cannot independently confirm that al-Afri is one and the same as al-Qaduli, but the U.S. government has said that one of al-Qaduli's aliases is Abu Ala. According to the State Department, al-Qaduli joined al Qaeda in Iraq -- the predecessor group to ISIS -- in 2004 and served as the group's deputy leader and its commander in Mosul. In February 2006, he traveled to Pakistan on behalf of al Qaeda leader Abu Musab al-Zarqawi to conduct an interview.
Al-Qaduli was captured in Iraq and jailed but released in 2012 and is said to have joined ISIS, spending part of 2012 in Syria, according to the U.S. Treasury.
Al-Afri is reputed to have a background as a physics teacher and to have been Osama bin Laden's favorite candidate for the top job after Abu Omar al-Baghdadi, the leader of the Islamic State in Iraq, as it was then called, was killed in a joint operation by U.S. and Iraqi forces north of Baghdad in 2010.
Analysts who track ISIS say al-Afri is from Tal Afar, a town held by ISIS in the north of Iraq and a crucial gateway for the transit of jihadis to and from Mosul. He is one of several ethnic Turkmens at the top of the ISIS hierarchy.
One theory for why he was passed over for the top job is that unlike Abu Bakr al-Baghdadi he was not from a family that could claim direct descent from the Prophet Mohammed.
Some analysts believe al-Afri has been maneuvering to lay claim to the top job.
Al-Afri delivered the sermon at Friday prayers in Mosul's al Zangi mosque last week, the same mosque Abu Bakr al-Baghdadi announced himself last July as the new "caliph," according to Hashimi.
According to an analyst in touch with jihadi sources in Syria and Iraq, al-Afri is attempting to repaint his family history to claim lineage to the Prophet Mohammed.
Some analysts believe al-Afri could only take-over in a caretaker role. Hashimi tells CNN that al-Afri could never take over as Caliph because he is neither Arab nor can credibly claim to be a descendant of the Prophet Mohammed.
Hashimi believes the next "caliph" will almost certainly have to have the appropriate lineage to the Prophet Mohammed. One of the prominent ISIS senior officials who can credibly claim such a lineage is Abdullah Alani, 51, a veteran Jihadi who joined al Qaeda in Iraq in 2004.
"He's one of only two credible options as the next leader of ISIS. He's well known and respected by (al Qaeda leader Ayman) al-Zawahiri and all the top Islamic leaders," Hashimi told CNN.
However, al-Zawahiri's opinion may not count for much. Although formerly subordinated to al Qaeda, ISIS split from its parent organization in early 2014. Today, al Qaeda's Syrian franchise, Jabhat al-Nusra, has declared all-out war on ISIS and there is scant indication of a rapprochement between the two jihadi groups.
Sheikh Younis al-Mashhadani
According to Hashimi, the other credible candidate as the next leader of ISIS is Sheikh Younis al-Mashhadani, a 55-year-old born in Baghdad who joined al Qaeda in Iraq in 2006.
He says that like al-Baghdadi, al-Mashhadani can trace his descent from the Prophet Mohammed through the Qureshi lineage.
Another valuable attribute is that al-Mashhadani has a track record as a religious scholar. For ISIS, the "caliph" should be the supreme political and religious leader of all Sunni Muslims. Like al-Baghdadi, al-Mashhadani has a PhD in Islamic studies from Baghdad University, Hashimi said.
Another factor favoring Mashadani is that he is one of the key figures on the ISIS committee that will select the next "caliph."
Abu Mohammed al-Adnani
Another possible candidate to lead ISIS is its current spokesman, Abu Mohammed al-Adnani, a 38-year old Syrian veteran of the Iraqi insurgency. Al-Adnani is believed to be the most powerful Syrian in the group and one of the group's key leaders inside Syria.
It was al-Adnani who first declared the emergence of a "caliphate" last June. Since then, al-Baghdadi has recorded only one video speech and one audio speech, but al-Adnani has made several audio recordings.
In September, he declared it was the religious duty of ISIS supporters in the West to launch lone-wolf attacks. The recording was a game-changer. In the months that followed there were ISIS-inspired attacks in North America, Europe and Australia. Al-Adnani renewed his call for attacks this past January.
The U.S. Department of State designated al-Adnani as a "specially designated global terrorist" on August 18, 2014, and last week offered $5 million for information on him. Al-Adnani joined al Qaeda in Iraq in the early days of the Iraq insurgency and fought in Anbar province. He was captured and spent time in custody in Iraq between 2005 and 2010, including, it is believed, at the U.S. detention facility, Camp Bucca.
According to analysts, two things may count against al-Adnani. One is that he is Syrian -- born in a village of near Aleppo -- whereas much of ISIS' top leadership is Iraqi. The other is his relative youth. It may also be too big a leap for him to be promoted from spokesman to leader. But if were to get the top job he would have instant name recognition among ISIS' supporters worldwide.
Other senior leaders
Abu Ali al-Anbari
Abu Ali al-Anbari is head of ISIS' Security Council and has substantial military experience, having been a senior intelligence officer in Saddam Hussein's army. Like al-Qaduli, he is from the northern Iraqi province of Nineveh.
Al-Anbari's role within ISIS became clearer after a raid last year on the home of another ISIS figure, Abu Abdul Rahman al-Bilawi, al-Baghdadi's military chief of staff for Iraqi territory. Memory sticks found during the raid, in which al-Bilawi, was killed, identified al-Anbari as directing military operations in Syria.
However, his previous experience in Saddam's military might make al-Anbari an unpopular choice among foreign fighters and more militant Salafists inside ISIS.
One problem with al-Anbari fronting ISIS would be his well-known background as an ex-Saddam Hussein military officer. Such, after all, would dilute the terror army's promulgated claim to be a purist Islamic organization rather than one composed heavily of former Iraqi Baathists. It may be that al-Anbari's role is better suited as kingmaker for the organization.
Abu Atheer al-Absi
As the head of ISIS media committee, Abu Atheer al-Absi is one of the five most powerful figures within ISIS, according to Hashimi. Little is known about al-Absi. According to Charles Lister, a fellow at the Brookings Institution in Doha, al-Absi served for a while as the ISIS "governor" of Aleppo.
Nima abd Naif al-Jubury
Nima abd Naif al-Jubury, or Abu Fatima al Jaheishi, is the current head of the ISIS military committee, according to Hashimi, one of the five top positions in ISIS. In February 2014, Saudi-owned news outlet al-Arabiya reported that al-Jubury had been in charge of ISIS operations in southern Iraq before relocating to the northern city of Kirkuk, which is now controlled by Iraq's Kurdistan Regional Government. His whereabouts are not known.
Abdul Rahman al-Talabani
Abdul Rahman al-Talabani is the head of ISIS's religious committee, according to Hashimi, another of the top five. There is little information on him.
Abu Bakr al-Khatooni
Abu Bakr al-Khatooni, is the head of the ISIS Shura committee, the top leadership body of the organization, according to Hashimi.
Abu Omar al-Shishani
Abu Omar al-Shishani (real name: Tarkhan Batirashvili), a former member of an elite Georgian military unit, has a reputation as one of ISIS's most capable military commanders, and is believed to be responsible for some of its key territorial conquests in Syria.
He reportedly saw action during the 2008 Russo-Georgia war, but then left the military and spent time in jail for the illegal possession of weapons. He traveled to Syria in 2012 where he led a fighting brigade from the Caucasus before pledging allegiance to al-Baghdadi the following year.
According to Hashimi, al-Shishani is now ISIS's special brigade leader.
Last week, the United States Department offered $5 million for information on him. In May 2013, ISIS appointed him the commander of operations in several provinces of northern Sryia.
According to the State Department, he has been a member of the ISIS Shura Council and "previously oversaw an ISIS prison facility in al-Taqba where ISIS possibly held foreign hostages" and "worked closely" with ISIS's financial section. Al-Shishani is unlikely to ever assume the top job of ISIS because he is not an Arab and has no pedigree as an Islamic scholar.
Shishani's strategic prowess is celebrated in ISIS and has been since he oversaw the taking of Menagh Airbase in Aleppo from the regime of Syria's Bashar al-Assad in August 2013. Since then, however, many of the Caucasian and Central Asian jihadis who have fought alongside him have questioned his savvy and the sensationalized media coverage about him.
Shishani relies almost exclusively on "cannon fodder" -- or suicide bombers -- to take terrain, one jihadist known as Khalid, who is now affiliated with Jabhat al-Nusra, noted on a Russian jihadi forum last year. "Umar Shishani is a person who is absolutely useless in military terms," Khalid wrote.
Opaque leadership structure
All these men appear to be still active and involved in the ISIS hierarchy, even though only one of them -- al-Adnani -- is ever heard by the outside world.
But divining the leadership structure of such a secretive organization is extraordinarily difficult. And ISIS has lost several key figures in recent months. In December last year, CNN reported that according to a senior U.S. military official, Abu Bakr al-Baghdadi's deputy in Iraq, Haji Mutazz (aka Abu Muslim al Turkmani) was one of several prominent ISIS officials to have been killed in recent airstrikes.
At the time, then-Pentagon spokesman Rear Adm. John Kirby said that since mid-November "targeted coalition airstrikes successfully killed multiple senior and mid-level leaders" within ISIS.
The constant pressure on ISIS makes any reliable analysis of its leadership structure more difficult, but analysts have no doubt that such a structured organization has a succession plan -- and the machinery to put a new leader in place swiftly should al-Baghdadi die.