Rodgers stated the Foxes have no motivation to sell at present:
"There's no pressure to sell and no need to sell.
"James is a very talented player and he will be here in January and beyond.
"He's a player we're keen to remain here and help us on this journey over the next years. James and his representatives are speaking with the club and these things take time."
Leicester have been the Premier League's surprise package this season and are in second place behind Liverpool.
Maddison has been a key performer for Rodgers this term, triggering United to make a January move for the blossoming 23-year-old.
The Red Devils are missing a productive No. 10, with only Juan Mata a suitable choice after an injury crisis at Old Trafford.
United have reportedly been interested in Maddison since last summer, and an ankle injury for Paul Pogba has stifled Ole Gunnar Solskjaer's creative options, prompting the coach to explore the market.
Rodgers added he would like to expand his options during the January transfer window, with the club reportedly linked with Liverpool's Harry Wilson—who has impressed on loan at Bournemouth.
"We want to add to [the] squad if we can," Rodgers said. "It all comes down to availability. We've got a really strong squad and lots of them are young players evolving. We want to but if we can't we'll continue with the squad we've got and look to reinforce in the summer."
The Foxes are on an upward trajectory, but it could be difficult for Maddison to resist United if the Red Devils make a substantial offer.
Solskjaer needs to find answers regarding his side's lack of consistency, and Maddison has proved he has the talent to play for a bigger club.
Per Steve Bates of the Sunday Mirror, United could reportedly offer £45 million plus Jesse Lingard for Maddison, with United prepared to pay the player £150,000 per week to move to Manchester.