UConn will never be a member of the Big 12. When the ACC chose Louisville that really hurt UConn in the conference change game. However the Big 12 would be smart add UC as soon they can along with another university. The problem for UC is that there really is no other university that they want to keep the conference even and allow for a championship game. BYU does not seem to have their affection, and the next best would be UCF.