Austin, 67, was the first and only Black man to lead U.S. Central Command, which oversees military actions in the region that includes Iraq, Afghanistan, Yemen and Syria.
Illinois Sen. Tammy Duckworth and Michele Flournoy, a Pentagon policy chief under former President Barack Obama, have also been mentioned as possible nominees to head Biden's Defense Department and many Democrats have called for a woman to lead the department.
Austin retired from the Army in 2016 as a four-star general and chief of Central Command, or CENTCOM. While in that post, he directed U.S.-led military intervention to counter the rise of Islamic State in Iraq and Syria beginning in 2014.
To serve as defense chief, however, Austin would need Congress to approve a waiver due to a law that requires any defense secretary to be at least seven years removed from active service -- a measure to ensure civilian control of the military.
"Waiving the law should happen no more than once in a generation," Sen. Jack Reed of Rhode Island, then the Democrats' ranking member of the armed services committee, said at the time. "Therefore, I will not support a waiver for future nominees, nor will I support any effort to water down or repeal the statute in the future."
Biden's reported choice of Austin has already drawn some criticism. Retired Army officer Jim Golby said in an op-ed in The New York Times that appointing another retired general would hinder the Pentagon's efforts to recover from instability during Trump's presidency.
"After a tumultuous four years, we need civilian leadership and a return to normalcy," he wrote.
"General Austin is a capable and respected former commander of Central Command, but he retired only in 2016. That's not long enough: A civilian -- not a recently retired general -- should lead the Pentagon.
"General Austin is a fine public servant, and he may well continue his service to the nation out of uniform. But the Pentagon would be the wrong place for him to do it."
A formal announcement is expected soon, perhaps as soon as Tuesday.