The Foxes are looking for a successor to Claude Puel, who was sacked on Sunday.
Rodgers, 46, has been in charge at Parkhead since 2016 and led Celtic to the title twice, while they are currently eight points clear of second-placed Rangers.
However, the former Swansea and Liverpool boss is understood to want to return to the Premier League at some stage.
And Rangers boss Steven Gerrard, who played for Rodgers at Liverpool, believes a return to the English top flight now will be too much for his old manager to turn down.
Gerrard said on Tuesday: “I’ve just been made aware that he’s in talks with Leicester. For us, we just see how that pans out really.
“It seems (the lure of Premier League has been a big factor) otherwise he’d have declined the opportunity to talk to Leicester.
“My focus right now is Rangers and we’ve got a big fixture tomorrow against Dundee. That’s my main concern right now but we’ll keep an eye on how it pans out across the road.
“I’m not really surprised by the timing because these things happen. Brendan has done ever so well at Celtic over the years so it’s no surprise that other clubs are watching him and wanting to acquire his services. He’s done a really good job and I’ve worked with Brendan so I know he’s a very good coach.”
Puel was fired in the wake of Saturday’s 4-1 home defeat by Crystal Palace, with Leicester slipping to 12th in the table.
The Foxes face Brighton on Tuesday evening still looking to pick up their first win of 2019, a miserable run which also saw them knocked out of the FA Cup at League Two Newport.
As well as two league titles, Celtic have also won three Scottish League Cups and two Scottish Cups under Rodgers.
If appointed the Northern Irishman will become Leicester’s third permanent manager since they sacked title-winning boss Claudio Ranieri in February 2017.