Morris played at Michigan under head coach Bo Schembechler. When Morris first arrived at Michigan, Schembechler told Morris (who stood five feet, seven inches) he was too short to play at running back. Schembechler recalled: "I told Jamie when we recruited him he was too small to be a running back and we wanted him for running back kicks. I did, however, promise him the chance to try to be a running back for us. Good thing I did, isn't it?" In his third game as a freshman, Schembechler put him in as the starting tailback, and he remained Michigan's starter at the position for four years.