Which conferences could they end up in over the next 3 years? I think we can agree that there is zero chance they end up in the P12 or SEC in the next 3 years. They are so far out of the B12 footprint, that barring a desperation move caused by pending B12 collapse, I don't see the B12 taking them (and the far-fetched scenario in which the B12 takes UConn means the B12 is on the verge of collapse anyway). So that leaves the B10 and ACC as power 5 conferences, plus the Big East.
The Big Ten's recent expansion has been for strategic market purposes. It is hard to envision a scenario in which UConn fits that growth strategy. Maybe the B10 could invite UConn & BC to expand into New England. But BC is tied into the ACC GOR agreement, and if there were an opportunity to break that agreement, the B10 would attempt to do that with 2 schools from Virginia/Carolina which is more aligned to the B10's strategic goals. About the only reasonable scenario in which I see the B10 taking UConn is if Notre Dame agrees to enter the B10 and the league just needs another school as a partner.
The ACC is certainly a possibility. If the ACC were to expand, then Cinci and UConn are probably the best targets for them. If they take only one school (for instance if UND joins for football, and they need a 16th school), Cinci probably gets the nod as a geographic partner for Louisville, especially with the expectation that BC would continue to balk at UConn. But I don't see the ACC needing to expand in the next three years. There is no strategic benefit for them adding UConn and Cinci (or UConn and anyone else).
So that leaves the Big East. And while the Big East might be a good fit for UConn basketball, it doesn't really solve the money issues that UConn has. Conference payouts in the AAC are greater than the Big East. Only Villanova in the Big East earned more than $3.0MM for the fiscal year ending June 2016. Only Navy in the AAC earned less than $3.5MM. And moving to the BE creates the problem of what to do with the UConn FB program. Dropping to FCS would only exacerbate UConn's financial issues, as their football program revenues would plummet without an offsetting decline in expenses.