Off the bat, no AAC or ACC team would schedule UConn as they are wholly owned ESPN properties. SEC, forget about it.
So you're looking at maybe two BIG games, two Big 12 games so say Illinois, Indiana, maybe a Kansas, Iowa State. Then the other independents that would need late in the season scheduling in BYU, Army, and UMass. Throw in an FCS game vs URI. That's 8 games and even that is a stretch.
I'm sure Fox wants UConn in the BE for hoop but not sure they have enough clout to help schedule 12 football games.