But two Bearcats players said Kelly told the team on Thursday that he wouldn't leave Cincinnati.
"He said, 'It's not an issue; I'm not going there,' " safety Aaron Webster said. "He said, 'I love Cincinnati, and I'm staying here.' "
When asked by an ESPN.com reporter after the game whether he had indeed told his players that, Kelly declined to discuss the issue. That also was his stance in the postgame news conference.
"I'm not going to talk about any job situations," said Kelly, whose team clinched its second straight Big East title. "I'm going to enjoy this victory.
"Let's talk about back-to-back-championship teams and these kids."
Kelly also chided the media for spreading what he called "misinformation" and added, "You folks need to get a handle on this, because it's ridiculous."
Kelly has been rumored to be one of Notre Dame's top candidates and told the ESPN this week that he would "entertain" a request from the Irish to speak to him after the Pitt game.
Wide receiver Mardy Gilyard said his coach was emphatic about not leaving in his talk to the team Thursday.
"He said, 'All this foolishness about me trying to go somewhere, that's just foolish,' " Gilyard said. "Coach Kelly, he made us strongly feel [he wasn't leaving]. It's almost like when your mom tells you the sky is blue, and you just know it's blue. You don't even have to look outside.
"With Coach Kelly telling us he's not leaving, we know he's not going anywhere."
Gilyard and Webster, both seniors, have heard that before. Former coach Mark Dantonio told them he wasn't leaving three years ago -- and then took the Michigan State job days later.
"There were different incentives then with Coach Dantonio," Gilyard said. "Coach Kelly always shoots it straight to us. In my opinion, I think he'll end up being the Bobby Bowden of Cincinnati, or our new Bob Huggins."
Brian Bennett covers the Big East for ESPN.com.