Just my opinion: UConn needs the Big 12 to have a 4-team expansion. As Dooley noted, if there's a 2-team expansion, then some combo of Cincinnati, Houston and BYU is highly likely. The 2-team expansion is what should scare UConn the most (regardless of who those 2 might be).
In the event of a 4-team expansion, it's an even greater bet that all 3 of Cincinnati, Houston and BYU get in. Now, I believe UConn has an excellent shot in that scenario where they would be the front-runner as school #4. However, the one school to watch out for is Colorado State. I'm not sure why so many reporters and analysts seem to be surprised at their inclusion on the Big 12 list of candidates: they're in a fast-growing state that the Big 12 really wants to be in (as the Denver market is quite possibly the #1 destination for Big 12 grads outside of the state of Texas... and that's even after CU had left) with solid academics, have a new football stadium being built and have synergistic value in a pairing with BYU to cover the mountain west region (which only has the Pac-12 as competition compared to the heavy competition with the Big Ten, SEC and ACC to the east). I don't see CSU getting into the Big 12 in a 2-school expansion, but they are a potentially compelling complement to BYU in a 4-school expansion (essentially avoiding the geographic outlier issue in the west that WVU has had in the east). Once again, Denver is a particularly key market for the Big 12 because the league's alums across-the-board are moving there in droves (unlike pretty much all of the non-Texas-based markets being considered in this expansion process). In a way, it's similar to why the Big Ten added Rutgers: they weren't looking for NYC to be a "Rutgers market", but rather a "Big Ten market" based on the synergy with all of the alums from Michigan, Penn State, Ohio State and other Big Ten schools that already lived in that market. There's a similar dynamic that's potentially in play with respect to Colorado State and the Denver market (where the actual CSU fandom there is less relevant than the Big 12 getting back direct access to a market where so many of their schools' alums already live).