The Foxes celebrated another trophy after they defeated Manchester City to win the Community Shield, following their FA Cup success from last season.
Maddison has been linked with a move to Arsenal in recent weeks, but Leicester boss Rodgers does not have any reasons to believe the attacking midfielder is leaving the club.
"I don't lose sleep over gossip and speculation," he said post-game, per the BBC.
"As far as I'm concerned, we haven't had anything for James.
"We're a club that develops players and staff, which means they're always held in high regard.
"James is a boy who has come here, developed and improved, and become a very talented player.
"He's enjoying his time here. Apart from that, there's not much more to say."
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