The story would have disappeared last week had West Virginia coach Rich Rodriguez not turned down Alabama's offer to replace Mike Shula, but since he did, the speculation about the Crimson Tide going hard after Saban surfaced again.
Saban acknowledged last week that Alabama officials had spoken to his agent, Jimmy Sexton, but Saban added that he told Sexton he was not interested.
Still, some reports have suggested Alabama might wait a few weeks until the end of the regular season to push hard for Saban.
King, meanwhile, brought up the Saban situation again during Sunday night's game between New Orleans and Dallas.
"I talked to Saban after the game and one of the things he said was, 'I have no intention of going anywhere other than to coach the Miami Dolphins,' " King said.
But King also added, "I gave him two opportunities to say flat out, 'I have no interest in the Alabama job,' He did say he has not talked to Alabama, but I gave him two opportunities, (and) he wouldn't take them."
ESPN's Kirk Herbstreit told radio station WQAM last week he had been told Alabama offered Saban a 10-year deal worth $57 million, while other reports suggested the offer was for somewhere around $35 million.
In the meantime, Saban keeps getting asked over and over again about Alabama.
"I in no way wanted to indicate to (King) or anybody else that there was any possibility of that. I have no intentions of going anywhere,'' Saban said.