No, I don’t think so. There is still some hostility left over from when the Southwest Conference broke up in '96 and TCU was not invited to join. At that point in time TCU had fairly mediocre football program, and was just beginning to start this modern era of competitiveness.
TCU has had to wander through the wilderness for years afterward, joining the WAC, the C-USA, then the Mountain West, so now that they have an invitation to the Big East, I doubt they will consider anything from the Big 12, and its equally doubtful that the Big 12 would offer it.
I don’t think the Big East is a good fit for TCU, for a lot of reasons…geographically it doesn’t make much sense, TCU has no historical ties/rivalries to any of those schools and many of the other sports that the Big East excels at, like basketball, are not particularly important at TCU. TCU has good programs in football, baseball, tennis, golf and a few other areas, but some sports that might be important on the east coast, like basketball, soccer, lacrosse, hockey, etc., just don’t register much at TCU.
So who knows how long they’ll stay in the Big East. But by the time they leave, the Big 12 may be non existent.