June 24 update: This is happening.
ACC, Pinstripe Bowl agree to 6-year deal starting in 2014, sources told @ESPN. ACC will face B1G in the bowl— Brett McMurphy (@McMurphyESPN) June 24, 2013
May 2 original: The Pinstripe Bowl will likely feature a matchup between the Big Ten and ACC after its current partnership expires. The ACC is reworking its bowl ties after losing the Chick-fil-A Bowl to the College Football Playoff, and the Pinstripe could be moved into its lineup, according to ESPN's Heather Dinich. The ACC's probable opponent in that game, the Big Ten, has been publicly interested in the Pinstripe Bowl for some time now. Neither conference has made an official announcement at this point.
The Pinstripe Bowl, which is played in Yankee Stadium, has featured a team within driving distance in each of its three games. With Syracuse and Rutgers leaving the Big East for the ACC and Big Ten, respectively, the new tie-in would make a lot of sense, as bowl executives have been pushing for local teams. The game is currently tied to the Big 12 and Big East, but the only "local" team remaining in either of those conferences is UConn.
Aside from the Pinstripe Bowl, Dinich reports the ACC could reconnect with the Gator Bowl, which they held a tie-in with until 2009, as well as replace the Big Ten in the Capital One Bowl.