Doege was 18 for 25 for 146 yards in the Red Raiders' 52-30 loss to Texas A&M on Saturday. Doege was relieving Taylor Potts, who lost a fumble and threw two interceptions.
"I thought he made routine plays and I thought he didn't try to make too much happen," Leach said of Doege. "He has a good arm and he is a sharp guy."
Junior quarterback Steven Sheffield is out with a foot injury.
On Tuesday, Leach said he would make a game-time decision on the position that has always been best for his program.
"It's disruptive," Leach said Tuesday, "but we just need to go out and get better and play better."
Joe Schad covers college football for ESPN.