In Syria, the number of Special Operations Forces is often in flux, but up to 300 are authorized to be in the country. In Iraq, there are 100 Special Operations Forces on the ground, according to the official.
US Special Forces in Syria are advising the Syrian Democratic Forces, which is made up of a number of local militias, including the Kurdish YPG.
Those soldiers are not generally advising the Syrian Democratic Forces side by side as they go into battle but typically advising and training them from behind the frontlines in northern Syria, according to the senior American defense official.
US Special Forces are also advising what the American military terms the "vetted Syrian opposition," numbering more than 1,000 fighters. The American defense official explained that that these forces "are volunteers. What they lack is military planning capability."
The aim of this training is not to build a conventional military brigade mirroring a US unit but to teach basic combat skills.
US Special Forces are instructing the Syrian volunteers in how to be infantrymen and use rifles and compasses. The volunteers are provided with a stipend.
A smaller number of the volunteers are also taught how to be forward observers for air strikes, which involves learning how to spot and report targets and also how to call in coordinates. That information may eventually result in US airstrikes once the information has been properly vetted.
US Special Forces are working with Turkish Special Forces to help train the Syrian volunteers.
As these Syrian forces advance towards Raqqa, ISIS' de facto Syrian capital, the hope is that more Arabs will join the Syrian opposition units, as Raqqa is largely an Arab city.
US military officials said they have been "soaking" Raqqa for a year with surveillance from drones and have been "building targets," such as IED production facilities.
A senior US defense official said the intent was to complete the "isolation" of Raqqa by Syrian Democratic Forces within the next few weeks and "certainly before the first of the year," at the beginning of 2017.
The senior US defense official anticipated that those members of ISIS who flee Mosul, which is now largely encircled by more than 100,000 Iraqi forces, will use smuggling routes that are thousands of years old across the Al-Jazirah desert, some heading west to the Syrian city of Deir al-Zour, not far from Raqqa, or south to the town of Al Qaim in Iraq or the Syrian-Iraqi border crossing of Abu Kamal.
US military officials said that ISIS fighters in Mosul have already deposited their families in Raqqa and Deir al-Zour. Local families in both cities have been kicked out of their houses in order to make way for the inflow of ISIS families.
The officials said that they expect that ISIS will make a last stand inside the city of Mosul on the west side, in the densely populated areas around the old city. ISIS has mined the bridges crossing the Tigris River and will blow them up they retreat to the western portion of the city, US military officials predicted.
Because western Mosul is heavily populated, air strikes by coalition planes and drones will have to be tamped down.
The coalition does not want to "rubbleize" Mosul as happened with the capture of the city of Ramadi in western Iraq when it was taken back from ISIS by Iraqi forces at the end of December 2015.