Could Texas be the team the Big 10 is eyeing to become the twelth member of the conference?
Maybe, but it's beyond unlikely Texas would do it. It's not so much that the Big 12 is so wonderful (all other factors being equal, Texas would rather be in the Big 10), it's that (at least for football) a move to the Big 10 would dramatically hamper Texas' ability to schedule. At all.
Texas would play eight conference games per season in the Big 10 each year. Add in that Texas would never drop Oklahoma and A&M from the schedule and the Longhorns have 10 games set for the season already. In all likelihood, that would mean two games with some combination of Rice, Houston, North Texas, Baylor and TCU to maintain a strong presence in the state, give local fans opportunities to see the team, and maintain their recruiting strategies.
And that's just football. As Brian notes:
Right. There's a reason Texas flirted with the Big 10 when the Southwest Conference disbanded - the academics at the member institutions are far superior to those in the Big 12 and it'd be a very strong financial situation for the athletic department in football.
But, there's a reason we went with the Big 12 in the end. For all the pros that exist for playing football in the Big 10 and being associated with better academic institutions, there are too many overall drawbacks when you consider non-revenue sports, travelling issues, and the "State of Texas" factor. (Our state pride - good in many regards - can make us a bit of a provincial bunch at times.)
All told, while the chatter is fun and the pros to playing football in the Big 10 are tasty, this is never going to happen. The Big 12, limitations and all, is a better fit for Texas athletics overall.