I doubt they will ever join the Big XII however the reason why they will not join the Big 10 is a moral one. It's a Catholic school and some Big 10 schools are involved in stem cell research which they are against. This has been their official stance on not joining the Big 10. They are in the Big East with their other progams however football wise it is a weak conference.
There are rumors that the Big XII is the most likely conference they would join however I don't see it. Outside of Texas and OU the rest of the conference is a bore. I personally really dislike the Big XII. It's a boring conference.
Kansas, Kansas State, Iowa State, OSU, Baylor, Mizzou ....

dude wake me up after all of those boring schools have been played.
What person that grew up in Texas could really get excited about those schools? There is zero history with the states of Kansas, Missouri, and Iowa. And Baylor? Most Baylor fans don't even take their football program seriously.
I could always get up for Nebraska, CU (sometimes), and of course A&M is always fun, now those schools are gone. So the only teams left that even make me want to turn on the TV is OU and Tech. The Sand Aggies only because their fans are pretty obnoxious and I like to see them get beat down.
So with that all said, why in the world would ND want to join the Big XII?? They would be locked into the same boring schedule.
Oh and BYU? Please, no excitement there either.
My excitement of college football is really taking a hit with Texas being in the Big Bore.
Kudos to A&M for joining a real conference. They might get beat down a lot however at least they are playing real teams almost every week. As a Texas fan I am envious. I would LOVE Texas to be in the SEC.