UT regents will vote on the matter when they meet Nov. 5-6, 2014.
The series sets up games between two of the winningest programs in NCAA history. Michigan ranks No. 1 in all-time wins with 912, while Texas is third with 876.
The lone previous meeting between the two schools came in the 2005 Rose Bowl following the 2004 season.
Texas won, 38-37, on Dusty Mangum's 37-yard field goal as time expired.
Vince Young accounted for 372 yards and five TDs, including 192 yards and four TDs on the ground, as the Longhorns won in their first BCS Bowl appearance to cap an 11-1 season.