At what point does this become a rivalry?
We will play Notre Dame every year in basketball so long as we both stay in the Big East. Given that Notre Dame is only offering its hoops team to the conference and Cincinnati is probably still thrilled to be in a BCS football conference, I don't see this arrangement changing anytime soon.
Speaking of Division I football, do you remember when Notre Dame stole our coach? Which might have been forgivable if he'd stuck around for (arguably) the biggest bowl game in Bearcat football history. [As a side note, a victory in the Papa Johns DOT com bowl doesn't exactly secure Kelly's legacy when compared to past greats coaching in Cincinnati.]
Although it's hard to imagine Kelly signing off on a home-and-home with his former team, the fact of the matter is that these two teams need to play each other often. South Bend is not far from the Queen City in D1 Sports miles, and the modern history makes even a matchup of mediocre teams ESPN2 worthy.
Rivalries have to have a starting point. The Miami-Cincinnati football rivalry escalated along similar lines. Ohio State now seems unwilling to acknowledge UC's existence. I'll gladly settle for Notre Dame.