Double-edged sword.
Fox likes us. Specifically, they like us anchoring their Big East product for 12-15% of what they would have to give us in the Big 12.
This is absolutely true and probably the thing that is keeping UConn out of the Big 12...
...But ESPN has some essentially wholly owned conferences. If ESPN likes UConn enough - and UConn football is good enough to curtail griping from certain members of these conferences - ESPN may pull the trigger on UConn.
Taking away the bargain Fox is currently getting on UConn also doesn't hurt the equation for ESPN. Fox should of course realize this, and with game theory and such start to weigh the option of losing UConn altogether.
Fox currently owns UConn's most valuable part (basketball). The question is whether ESPN would be willing to pay for the whole package, and if Fox is willing to let that happen and potentially lose UConn altogether. Football improvement dramatically helps that whole package equation.