In my opinion, there is only one institution who knows the answer to this - the LDS, or the Church of Latter-Day Saints. For those who don't know, that's the Mormon church, and BYU is a Mormon school. Ultimately, the LDS will decide what BYU's future will be - not BYU's athletic department, not the faculty or students, not ESPN. What it boils down to is, what benefits would BYU see from joining the Big East for football only? Why should they surrender their new status as an independent? They have an exclusive contract with ESPN, their own television network (BYUtv), and a nationwide fanbase. Sure, scheduling is tough when you're independent, but that hasn't stopping BYU thus far, and even then, how appealing would a Big East football schedule be to a team like BYU? They don't even fit in with the Big East culture (whatever that may be).
Right now, the Big East is in exclusive negotiations with ESPN regarding their television contract. No one really knows how much money each Big East school will be making in several years. It is likely going to require a big pay check to attract BYU to the conference (according to Brett McMurphy, BYU's contract with ESPN is worth approximately $4 million annually, unless he just pulled that number out from his rear-end). Even if the Big East's contract is worth $10 million per school, I'm still not confident that figure is high enough to attract BYU. In addition, BYU wants to keep their 3rd tier rights, something the Big East is reluctant to agree to (correct me if I'm wrong here). Unless the Big East can throw a lot of money at BYU, the two simply cannot see eye-to-eye long enough to work out a mutual agreement. The only reason I wouldn't rule out BYU joining the Big East is simple: bowl access.
The recent announcement of a 7th playoff bowl game, to feature the best of the "little guys" vs. one of the power conference schools, is what may ultimately force BYU to join the Big East. For some reason, many BYU fans seem to think that if they remain independent they will lose access to the football playoffs. I personally don't think that will be the case, as Notre Dame made provisions so they could participate when they were still fully independent, before the ACC deal. Why would any independent team be denied access to the 7th bowl game if they are ranked very high and have 0 or 1 losses? I can't see a 10th ranked, 11-1 BYU being shut out of the 7th bowl game if they are ranked higher than any of the non-power conference teams. So do they really need to be in the Big East to ensure a spot in the playoffs? Joining the Big East and winning the CCG would be the most straightforward path to the playoffs for BYU, but is that really much easier than staying independent and trying to go undefeated? I don't think so. BYU is no Notre Dame, however, and there are no guarantees they will be respected as an independent, even though they do have one national championship (1984) to hang their hat on.
While the Big East may be confident they can land BYU as their 14th football member, I really just don't see it happening. If BYU can survive and thrive as an independent, why give that up? Even then, aside from San Diego St. and Boise St., there are no other west coast teams - how appealing could that possibly be to BYU? BYU is making plenty of money as it is, and unless the Big East scores a television contract which is worth as much or nearly as much as the ACC's, I just don't see any strong argument for BYU to join. They didn't want to last year, and I don't think the landscape has changed enough now to make them join. And if they do join, it'll probably be because of that 7th bowl game. The question is, how much longer until a decision is made?