If Lunt chose a Big 12 school, he would also forfeit a year of eligibility.
A source told The Oklahoman that Notre Dame coach Brian Kelly has inquired with Lunt's high school coaches in Rochester, Ill., about potential interest in the Irish.
Still, Lunt's possibilities for playing for a power-conference school have dwindled. Same for Southern Miss and Central Michigan, the latter of which is on OSU's schedule in 2015 and 2016.
Lunt won the starting job last spring, just months after leaving high school early. Injuries interrupted his season, with Clint Chelf finishing the season as No. 1 and J.W. Walsh the backup.
This spring, Gundy first named Chelf the clear starter, then recanted, saying the three-way competition was ongoing. On May 9, OSU revealed Lunt's decision to transfer.