School spokesman Larry Leathers confirmed Franklin called Saban on Wednesday afternoon to apologize.
The Vanderbilt coach spoke Monday night at the fall sports banquet for Central High in Macon, Ga., where linebacker Nigel Bowden is one of his top commitments.
According to videotape from WMAZ-TV, Franklin said, "There's this guy in Alabama. I think his name is Nicky Satan. You guys have probably heard of him before. I'm going to outwork him. I'm going to outwork him. And that's kind of our plan every single day."
Franklin told The Tennessean his comment was meant strictly as a joke about a coach who has won four national championships.