Lunt had been considering transferring to all three schools, a person familiar with his plans told ESPN this week. He can still visit and consider the other two schools on his list, Illinois and Louisville, sources said.
CBS earlier reported that Oklahoma State had trimmed Lunt's list.
These decisions are often based on the possible transfer destination being in-conference, being on a future schedule or if the head coach believes contact between another staff and the player was made before a release was granted.
Oklahoma State does not have any games planned against the three banned schools.
Coaches Tim Beckman (Illinois), Charlie Strong (Louisville), Butch Jones (Tennessee) and James Franklin (Vanderbilt) have all previously recruited or have a relationship with Lunt.
Lunt began last season as the Cowboys' starting quarterback as a freshman. Leg and head injuries sidelined him for part of the season, when he threw for 1,108 yards, six touchdowns and seven interceptions.
Lunt will consider proximity to his Illinois home, as well as the relationship with the coaches he'd be playing for when deciding on where to go, according to a source. The source also said Lunt would have liked more communication about where the quarterback competition stood while Lunt was at Oklahoma State.