Gwynn received scholarship offers to play college basketball, but none for college baseball. He also went unselected in the 1977 MLB draft, which Gwynn attributed to his limited playing time. He wanted to play both sports for Cal State Fullerton, which was okay by basketball coach Bobby Dye, but baseball coach Augie Garrido did not believe an athlete could handle both sports in college. San Diego State basketball coach Tim Vezie wanted Gwynn to commit to playing two years of basketball before playing baseball. Gwynn also had an offer from Texas Christian University (TCU). However, he was told that he would be their first black player in 30 years, which ruled them out from his consideration. He chose to attend SDSU, calling it "the best option I had".