Saban, a former defensive coordinator with the Cleveland Browns under Bill Belichick in the early 1990s, has been considered a hot commodity for a few years now.
He turned down the chance to coach the Chicago Bears last offseason, presumably because the Bears wouldn't grant him authority over personnel matters.
In a radio interview last month, Saban said he didn't necessarily have to have personnel authority to considered an NFL job.
Saban, who is busy preparing LSU for a Jan. 1 bowl game against Iowa, said he wasn't planning on discussing the meeting after his team's practice on Wednedsday, but he did release a statement.
"I owe it to the people of Louisiana and the fans of LSU football to let them know I have had a preliminary conversation with the Dolphins to exchange ideas about their head coaching position," Saban said in the statement. "No decisions were made in this meeting and they will continue their search for a coach. I will continue to be committed to LSU, our football program and totally focused on our bowl game versus Iowa."
Ironically, LSU athletic director Skip Bertman was a baseball coach at the University of Miami at one time.
"We are all aware that other NFL teams have made overtures to him in the past and he hasn't expressed any interest," Bertman said of Saban. "But this is one of the premier jobs in the NFL and he owes it to his family and their future to hear what the Dolphins have to say."
Dolphins interim head coach Jim Bates was on that Cleveland staff with Saban in the early 1990s and he called Saban a "personal friend" and a good football coach.
Bates said he would like to be considered for the head coaching position on a full-time basis, but said he had had no discussions on the subject with Huizenga.