According to Leicestershire Live, the London outfit now see Rodgers as a prime candidate to take over at the Tottenham Hotspur Stadium, with Antonio Conte and Brighton & Hove Albion boss Graham Potter also linked with the post, given that the Lilywhites hierarchy are reportedly unhappy with Santo's performance this season.
The Leicester manager has been quick to distance himself from other roles in recent weeks though, telling reporters: "I don't even think about it (Manchester United links) - and that's the brutal honesty. I'm sure the supporters are probably tired of it. At Leicester, there is always a link. My focus is always here with Leicester and developing the football club on to that next level, where you're competing for European football and challenging for honours."
Following a 3-0 loss to Manchester United on Saturday, Tottenham now sit eighth in the Premier League, with pressure reportedly heaping on the former Wolverhampton Wanderers manager, who took the reins in the summer.
Rodgers, meanwhile, has guided the Foxes to consecutive fifth-placed finishes in the top flight, and they finished four points clear of the Lilywhites last term.