Lallana, 31, is out of contract in the summer and it has been reported that the Foxes have made enquiries with his representatives.
But Rodgers, in charge at Anfield when Liverpool signed Lallana from Southampton for £25million in 2014, insisted no contact had been made.
“I’ve seen a lot of stuff around Adam and that we’ve approached Liverpool and what not, which obviously isn’t the case,” said Rodgers, whose side take on Manchester City at home on Saturday.
“But Adam is a wonderful player and not only that he’s got a great attitude.
“When I took him into Liverpool he was unfortunate early on with injuries, but he showed when he’s fit and available he’s a fantastic player.
“He’s at the stage of his contract where he will have options I’m sure.
“But certainly what’s been put out there over these last few days, it’s not the case.”
They have slipped four points behind City and will bid to close the gap in an evening kick-off at the King Power Stadium.
Rodgers, meanwhile, has called on the game’s authorities to simplify the rules surrounding offside and the video assistant referee.
Arsene Wenger, FIFA’s chief of global football development, has proposed a new ruling, which would mean a player would be deemed onside if any part of his body is level or behind the last defender.
“It’s something to discuss,” Rodgers added. “We’re probably sat here now in more controversy with VAR and refereeing than we’ve ever had.
“The whole idea was to make it easier, make it simpler for the game, so probably one or two things need to happen.
“Yes, they need to change the rules, or you make the technology better. For me it all seems a little bit complicated.”