The NCAA won't let them have a conference championship game with only 10 members. It also appears that the Big Ten, ACC, and SEC have pretty much secured their members, so it's very unlikely at this point that the Big 12 would get any candidates for expansion from those conferences. That leaves the Big East remnants, CUSA, or teams in the West such as BYU and Boise St. From that group, it appears that BYU would be given serious consideration.
I am NOT in favor of BYU joining the Big 12 for all sports. However, I'd be VERY happy with a FB-only offer for BYU and BSU to join the B12. As others have stated, there are rumors that ESPN would favor this kind of arrangement.
My list of preferred end-states for BYU:
1. Pac-12 for all sports
2. B12 FB-only, WCC for other sports
3. Current situation--Indy for FB, and WCC for other sports
4. B12 for all sports
5. Forming new conference for all sports to include some of the best of the MWC and CUSA
6. Re-joining MWC for all sports with specific benefits for BYU enumerated in the contract
I'm pretty happy with BYU's current situation. I highly doubt the Pac-12 would ever invite BYU, so I don't even realistically consider that as a possibility. That leaves the B12 for FB only, with the other sports staying in the WCC. I would LOVE this outcome, especially if it included some sort of scheduling agreement with B12 teams for basketball, perhaps something like 4 games a year, 2 in the MC, and 2 on the road.