Doug Nussmeier left the Crimson Tide on Thursday to become offensive coordinator on Brady Hoke's staff at Michigan.
The 38-year-old Kiffin visited with Alabama coach Nick Saban prior to the Sugar Bowl "to share ideas and exchange ideas ... [for] professional development," Saban said at the time.
"Lane is a really good offensive coach, and I've always had a tremendous amount of respect for him," Saban said then. "Just to come in and brainstorm a little bit to get some professional ideas with our guys is a really positive thing."
Kiffin was fired by USC in late September after a 62-41 loss at Arizona State. He registered a 28-15 record with the Trojans following a one-year stint at Tennessee, where he was 7-6.
Nussmeier helped the Tide to averages of 38.2 points and 454.1 yards per game this season.
Joe Schad of ESPN contributed to this report.