Sterling was selling CDs early Tuesday outside the Triple S Food Mart in Baton Rouge, the source said, when the homeless man approached him and asked for money.
The man was persistent, and Sterling showed him his gun, the source said.
"I told you to leave me alone," Sterling told the man, according to the source.
The homeless man then used his cell phone to call 911.
The details about the 911 call shed new light into the Baton Rouge police's high-profile fatal shooting of Sterling, a 37-year-old black man.
A graphic cell phone video of the shooting was shared widely on social media, quickly sparking local protests and drawing national attention. Federal authorities have taken charge of the investigation.
Sterling was shot outside the Baton Rouge convenience store after an encounter with two police officers. The officers can be seen in the video on top of him before shots were fired.
Local civic leaders and Sterling's loved ones have promised to find out what happened.
"I, for one, will not rest," Quinyetta McMillon, the mother of one of Sterling's children, said Wednesday, "and will not allow ya'll to sweep him in the dirt."
The 15-year-old son of her and Sterling stood by his mother's side, sobbing.
A criminal investigation, led by the U.S. Department of Justice, is underway in Sterling's death, Gov. John Bel Edwards said Thursday night at a prayer vigil in Baton Rouge. The FBI and state police also will be involved, he said. A federal civil rights investigation also will conducted.
Edwards dismissed any questioning of Louisiana's decision to hand over the investigation to the Justice Department.
"We're not abdicating anything," the governor said, adding that "we're making the best decisions to make sure that the situation remains under control here in Baton Rouge and that we don't experience any more upheaval ... in our communities here in Baton Rouge and around Louisiana."
One of the crucial next steps will be to determine what happened before the confrontation ensued Tuesday.
Authorities said the officers were responding to the 911 report of a man with a gun. A source close to the investigation told CNN the 911 caller said Sterling was "brandishing a gun."
A law enforcement source with knowledge of the investigation told CNN that the officers pulled a gun from Sterling's body at the scene. No further details were provided on the type of firearm.
Abdullah Muflahi, the owner of the Triple S Food Mart, told CNN he wasn't aware of any incident Tuesday that would have spurred such a call.
But he's sure the shooting was caught on his store's surveillance cameras, though he hasn't seen it. Police took the video later Tuesday, he told CNN.
There also is police body camera footage of the shooting -- even though the cameras were dislodged -- Baton Rouge police Lt. Johnny Dunham told reporters Wednesday. The cameras continued to record, he added. A law enforcement source told CNN that the cameras fell off during the scuffle.
Investigators said they'll review multiple videos of the shooting, and they're canvassing for witnesses.
Authorities haven't said what those police videos or other surveillance footage of the scene show, including the lead-up to what the public has already seen or the possible weapon-brandishing incident.
The source involved in the investigation told CNN that the other videos are not nearly as clear as the bystander videos.
Together Baton Rouge, a community group, held a press conference Thursday, applauding the Justice Department for jumping on an investigation and urging the probe to be as broad as possible.
The Rev. Lee Wesley, pastor of the Community Bible Baptist Church, and another community leader, Edgar Cage of the Episcopal Diocese of Louisiana, said they hope that any investigation goes beyond just focusing on possible civil rights violations and explores other facets, including systemic problems on the local police force.
Attorneys for McMillon, the mother of Sterling's son, are demanding "transparency."
"Our primary mission is to provide this grieving family with the answers they are seeking regarding the senseless shooting death of Alton Sterling. Thanks to multiple videos that captured the horrific incident, we know far more than we typically would, but many questions still remain," attorneys L. Chris Stewart and Justin Bamberg said in a statement.
The two said they have handled other "high-profile tragedies at the hands of law enforcement."
"We appreciate the hard work and dedication of the vast majority of members of law enforcement. But when they fail to follow their extensive training and unnecessarily take a life, they must be held accountable. No police officer should be above the law."
Two videos appear
There are two videos that have publicly surfaced showing Sterling's killing -- the one that catapulted the case into the national spotlight Tuesday, and a second, shorter video of higher quality recorded closer to the shooting.
The first video was posted online Tuesday night. It begins with the camera facing a car dashboard as the three men stand near the vehicle. A single pop is heard. Then someone yells, "Get on the ground."
An officer pulls Sterling over the hood of a silver car and pins him to the ground. Once he's down, the officer begins to assist a second officer in restraining him.
Yelling ensues, though it's hard to make out what's being said. Then there are two bangs.
Witnesses inside the car shout and swear. Three more bangs go off. A woman in the car starts crying.
The second video shows Sterling already on the ground, on his back. One officer is kneeling to Sterling's left. The other officer appears to be straddling Sterling's legs. Sterling can be seen from the chest up, and his lower legs are also visible. His left arm and hands are not visible; his right arm is by his side.
After gunshots are heard, the camera pans to the right, then back to Sterling, who has a large blood stain on his chest. The officer who was on his legs now lies on the pavement above Sterling's head, his gun pointed.
The officer radios for an ambulance. As Sterling moves his left arm toward his face and then his chest, the other officer appears to remove something from one of Sterling's right pockets. Baton Rouge police Chief Carl Dabadie Jr. said Sterling was armed at the time he was killed and one witness said the officer removed a gun from Sterling's pocket.
The officers involved in Tuesday's shooting -- Blane Salamoni and Howie Lake II -- have been placed on administrative leave. A source close to the investigation told CNN the officers were interviewed Tuesday night.
Tensions are running high in the city of 238,000 people as officials vowed to be transparent about how they handle the controversial case.
"The individuals involved in his murder took away a man with children who depended upon their daddy on a daily basis. ... As this video has been shared across the world, you will see with your own eyes how he was handled unjustly and killed without regard for the lives that he helped raise," said McMillon, the mother of Sterling's son.
Edmond Jordan, an attorney representing Sterling's family, said the first video of the shooting raises troubling questions.
"I think that the city is going to have to give us some good answers," Jordan, who is a Louisiana state legislator, told CNN. "And I don't know if they'll be able to."
The 'CD man'
Sterling was known as the "CD man," a laid-back guy who would sell tunes and DVDs outside the convenience store where he was shot, according to local media.
"Alton was a respected man. He was beloved in the community. He did not deserve the treatment and this excessive force that was exerted on him by the police department," Jordan, the Sterling family attorney, told CNN.
Muflahi, the store owner, said he'd known Sterling for six years and never saw a confrontation between Sterling and anyone. Sterling never got into fights, he said.
"Just five minutes before (the shooting)," Muflahi said, "he walked into the store getting something to drink, joking around, (and we were) calling each other names."
Sterling had earlier encounters with law enforcement.
In 2009, he was charged with carrying a weapon (a firearm) while in possession of a controlled substance (marijuana). He pleaded guilty two years later and was sentenced to five years in prison, with credit for time served and a recommendation of work release and drug treatment.
There's no evidence that officers who responded to the convenience store early Tuesday were aware of his criminal history.