Kiffin turned the job down, sources said, in the days leading up to the Crimson Tide's 45-40 victory over Clemson in the College Football Playoff National Championship presented by AT&T.
In Phoenix two days before the title game, Kiffin was asked what opportunity it would take for him to leave Alabama.
"I have a great job," Kiffin said Saturday. "So anytime that stuff comes up, I remind myself that I have a great job with great players and a great head coach, and there are only two teams still playing, so we're fortunate to be here."
UCLA coach Jim Mora worked with Kiffin's father, Monte, in 1995 when they were with the New Orleans Saints.
In 2013, after Kiffin was fired as USC coach, Mora, on "The Dan Patrick Show," said he would hire Kiffin if he ever were available.
"Yeah, but I don't have a position on my staff," Mora said in October 2013. "I love my staff. I've got Noel Mazzone as my offensive coordinator. In my opinion, he's one of the best in the business. If there's ever a situation where Lane was available and he was interested and there was a position available, he's a guy anyone would want to consider.
"He's [Kiffin] a good football coach. He's a really good playcaller. I've had to scheme up against him on defense, and when he's got the quarterback he thinks can make it happen for him, he's tough to defense, because he's not predictable. He gives you wrinkles, and he sets you up, and he's a good playcaller."
Earlier this month, Mazzone left UCLA to be the offensive coordinator at Texas A&M.