ND is not run by the football team. It cares a lot about academics and ethics (even if it views ethics differently than others). Because of that, it will not join the Big12. Baylor is the only school ranked higher academically than the ACC's lowest school (Louisville) and the B10s lowest three schools (all new additions in the last 25 years), but none of the long-term schools.
Academics will be the SEC's biggest hurdle to pull ND. SEC is held down by Miss St, Ole Miss, Bama, and LSU. If we can get North Carolina and Virginia, then it will increase the odds of ND looking south. Miami and USC are established ND rivals and rank high academically and would also help. At that point, the conference would be huge. It will be more like the NFL.
USNWR ranking
Notre Dame 20
Virginia 26
North Carolina 26
USC 28
A&M 51
Miami 64