So DJ's had a couple of Skull Sessions recently that have discussed the possibility of Oklahoma joining the Big Ten. Just to add to that a bit, I have a former co-worker who spent part of his childhood in Oklahoma and has very strong family ties there. As a result, he is a very passionate Oklahoma fan. We still talk every once in awhile, and a couple of weeks ago, he said that down there, word is going around that representatives of OU and Kansas sat in on some Big Ten meetings.
I did some quick research and it seems like a strong possibility, as both OU and Kansas have relatively strong athletic programs. An important factor is who is a member of the prestigious Association of American Universities, a group of excellent academic schools that place a focus on research. Every Big Ten member is a member of the AAU except Nebraska (They were until 2011, so they were when they joined the conference). The Big Ten conference has said before that membership is highly important to them. This is a strike against Oklahoma but a plus for Kansas as well as Texas. Obviously, Texas is the crown jewel of the bunch with their high academics, large avid fan base, successful athletic department, recruiting area, market, etc. but their location is the worst of the three. Oklahoma will obviously want to stay with Texas if possible (they would want to stay with Ok St. as well, but I do not see OK St. joining anytime soon). Kansas maybe makes the most sense because of their membership, location, and strong athletics (outside of football obviously).
The problem is, because conferences are only allowed to have 16 members, the Big Ten can only take two teams even if they wanted to. I think that we eventually will, but who do you take? A lot will boil down to how much the league cares about membership in the AAU. They say they care a lot. This really puts Oklahoma at a disadvantage. It is widely assumed that realignment for all major conferences will not happen until most TV deals expire, which is around 2022 and 2023, so there is some time. If I had to pick, I would probably take Texas and Kansas. I would also put Texas as the least likely of the three. The chances of any of this happening in the next year or two is highly unlikely, but it's still interesting to look at!
EDIT: There is no 16 team rule. I previously thought there was. Apologies.