Coffman, who came to Indiana as a junior college recruit, became the starter in 2012 after Tre Roberson was injured, and he threw for 2,734 yards with 15 touchdown passes and 11 interceptions.
He was third on the Hoosiers' depth chart in 2013 behind Roberson and Nate Sudfeld.
Indiana coach Kevin Wilson said in a video posted on the Hoosiers' website that he is trying to help Coffman find a new school where he can get more playing time.
Wallace, a 6-foot, 234-pound linebacker, did not play last season after getting a medical redshirt in 2012. The Indianapolis native is expected to land at Indiana State, a Football Championship Subdivision school, and will not have to sit out.