Coach David Beaty sounded hopeful Tuesday that Willis will play Saturday at TCU.
Last year's starter, Michael Cummings, sustained a season-ending knee injury in the spring game, while backup Deondre Ford had season-ending surgery to his thumb. That leaves only Willis, redshirt freshman Keaton Perry and transfer T.J. Millweard on the roster.
Freshman quarterback Carter Stanley has been redshirting.
Willis, a freshman, has been impressive enough at times that Cozart could transition to wide receiver when he does return next season. The Jayhawks are thin at the position, and Cozart is one of the best athletes on the team.