Maddison, who the Gunners allegedly value in the region of £60m, is said to be open to a transfer to the Emirates Stadium this summer.
However, at a time when the two clubs are likely to be some way apart regarding a potential fee, Rodgers has played down talk of the Foxes losing their chief playmaker.
Speaking to reporters, Rodgers said: "I know he is very happy here and he wants to be here. If anything comes to the club, Jon Rudkin (director of football) would tell me straightaway and I would deal with it then, but there has been nothing that's come my way.
"I've not been told anything to say [he won't stay]. He is happy in training and he is working hard, and he is a talented, important member of the squad. He had his season disrupted by injury last year but hopefully this season he can show what a real top player he is."
Arsenal have reportedly already failed with a proposal which included at least one fringe member of Mikel Arteta's squad. body check tags ::