Kiel announced last month he would transfer from Notre Dame.
Kiel, who spent one season with the Irish, said he has been contacted by Ole Miss, Mississippi State and Kansas State, and that Tennessee, Ball State, Northern Illinois and Miami (Ohio) are also options. Kiel said he's not sure which school he'll visit next.
"The biggest factor for me now going through it all again is having a great relationship with my position coach," said Kiel, adding that he knows he'll have to sit out another season, so he wants to go to a program where he can compete for the starting position in 2014.
Kiel, 6-foot-4, 210 pounds, was one of the nation's most-recruited players after a stellar career at Columbus East High School in Indiana. But Notre Dame redshirt freshman Everett Golson won the starting position and led the Irish to the national championship game last season.
Kiel said he plans to make a transfer decision at the end of spring football, which is at the end of April. After high school, Kiel committed to Indiana, and then LSU, before settling on Notre Dame.
"This is something you don't want to do," Kiel said. "But at the same time, I'm doing what's in my best interest and to get on the field."
Kiel said his weekend trip to Cincinnati was "a great visit. A lot of fun."