The official, speaking on condition of anonymity, said General Joseph Votel would be nominated to lead Central Command, whose area of operations include Syria, Iraq and Afghanistan.
His nomination would reflect the increased role special operations troops are carrying out in the region.
Obama has repeatedly said he doesn't want large-scale American deployments in Syria or Iraq, and instead has been relying on air power and smaller units of elite specialists to partner with local forces fighting Islamic State jihadists.
Austin has kept a relatively low public profile as CENTCOM head.
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In September, he appeared before the Senate Armed Services Committee, where lawmakers blasted him over the pace of the anti-IS fight and allegations that senior military officials altered information to downplay the strength of IS fighters and Al-Qaeda's branch in Syria.
Votel's planned nomination was first reported by the Wall Street Journal. The White House did not immediately confirm the possible nomination.
The Pentagon last year announced it was sending about 50 special operations commandos into Syria to conduct raids, gather intelligence and work with local forces.
In October, US special operations troops and Kurdish peshmerga stormed an IS-run prison near Hawijah in northern Iraq, freeing some 70 captives who were facing imminent execution. One US fighter died in the operation.