Bookmakers have put them at the shortest odds to sign Maddison, who is attempting to leave Norwich City this transfer window.
Maddison managed 14 goals and eight assists for Norwich in the Championship last season.
With the club only finishing 14th, Maddison is hoping that he can secure a move to a Premier League club.
Sky Bet have put Leicester at 8/13 odds on signing Maddison, which is ahead of Liverpool on 4/1 and Huddersfield & Tottenham at 16/1. The player is rated at 1/3 to leave Norwich.
Leicestershire Live believes that Maddison is a serious target for the club this summer, but the £30 million price tag put on his head by Norwich may put them off.