Jefferson suffered an ankle injury in the loss to the Tide. The ankle was injured on a third-quarter sack, and the sophomore did not return.
Head coach Les Miles seemed cautiously optimistic that Jefferson would be ready for the Homecoming game against Louisiana Tech this Saturday.
"Jefferson took snaps, took throws," Miles said. "He was a little gimped, but getting better. We'll kind of know more as we go forward. To be honest with you, I do feel good about him."
If Jefferson is not able to go, Jarrett Lee would get the start.