Rodgers is allegedly currently house-hunting in Cheshire, with the 20-time English champions identifying him as the head coach to lead the team forward.
The 48-year-old has won two trophies during his time at the King Power Stadium, securing last term's FA Cup before lifting the Community Shield earlier this season.
Rodgers has managed Watford, Reading, Swansea City, Liverpool, Celtic and Leicester since his first coaching position with Chelsea reserves in 2006.
The Northern Irishman could now be heading for Manchester, and with that in mind, Sports Mole takes a look at how Man United could line up under the Leicester boss, who could be in the job before Christmas.
Jadon Sancho has really struggled to get going in the early stages of his Man United career, and Rodgers will surely be determined to help the England international regain some confidence, so it would not be a surprise to see him given a regular run in the side on the right.
Rodgers would want to use Edinson Cavani as much as possible, but there is no getting away from the fact that the Uruguay international picks up a lot of injuries, so a 4-3-3 formation could see Cristiano Ronaldo start at the tip of the attack, with Marcus Rashford and Sancho out wide.
Bruno Fernandes and Scott McTominay are likely to feature regularly in midfield, while it seems unlikely that Rodgers would disrupt the regular back four in terms of personnel, but the Northern Irishman would certainly believe that he could improve the shape and aggressiveness of the defensive unit.
The main beneficiary at Man United could be Donny van de Beek, who has never convinced Solskjaer that he deserves a run in the side; Rodgers might feel differently, though, and the Netherlands international is still more than capable of securing a long-term career at Man United.
The 24-year-old would surely benefit from Rodgers's coaching style, and he could be given the confidence to become an important player for the 20-time English champions moving forward.