Rodgers was linked with the Arsenal job earlier this month after the Gunners axed Unai Emery.
However, the Northern Irishman signed a new contract with Leicester to prove he is committed to the project.
But to continue building for the future the ex-Celtic boss must keep hold of his main men.
A precedent was set in the summer when Leicester did not want to sell Harry Maguire to United.The centre-back eventually got his move, albeit Solskjaer’s side had to stump up a world record fee for a defender (£80m).
If Leicester take the same stance in January then Maddison may cost a similar amount.
However with the title race now over the midfielder’s head could be turned if a blockbuster bid comes in.