The Foxes are in the market for a new boss after taking the decision to part with Claude Puel.
Former Liverpool and Swansea boss Rodgers has emerged as their top target on the back of a trophy-laden spell in Scotland.
Reports are suggesting that the Northern Irishman has agreed to return to English football, with Neil Lennon being lined up for a return to Parkhead as his successor.
Former Celtic striker John Hartson believes Rodgers will be making a mistake if he does head to the King Power Stadium, with Leicester representing a step down from the Glasgow giants.
The Hoops legend told the Evening Times: “I see the attraction of Leicester. They are very wealthy. They play in one of the top leagues in the world and there would be money to spend.
“But I would still argue that in terms of clubs, Leicester are nowhere near Celtic. And I say that with the greatest respect.
“And I know I have said it before, but for me it is vital for Brendan to leave a legacy at Celtic.
"He can be the man not just to take them to 10-in-a-row but to 11, to 12, to 13, to 14… if the board go on and back him this summer then it could be anything.
“There could be no let up to just how dominant Celtic are in a domestic sense.”
This is not the first time that Rodgers has been linked with a return to the Premier League.
He was mooted as a candidate for Arsenal as they mulled over their options in the wake of Arsene Wenger’s decision to step down from a post he had occupied for 22 years.
Rodgers stated amid that speculation that he was fully committed to his post in Scotland.
It is, however, now being reported that he has had a change of heart and will be heading back south of the border.
If he does walk away from Celtic, then he will leave with two treble successes to his name, with the Bhoys currently in the hunt for a third in succession after already landing the Scottish League Cup while reaching the Scottish Cup quarter-finals and sitting at the top of the Premiership table.