The 22-year-old has entered the final six months of his contract and is therefore free to enter into discussions with foreign clubs this month over a move at the end of the season.
There have been suggestions that Marseille are open to a sale this month, with the Ligue 1 outfit reluctant to lose the Frenchman on a free transfer ahead of the 2022-23 campaign.
Man United have long been linked with the midfielder, and according to Corriere dello Sport, the Red Devils have 'come forward' for his signature.
The report claims that the 20-time English champions are now exploring the possibility of bringing him to Old Trafford before the January transfer window closes for business.
Kamara has again been an important player for Marseille this season, making 23 appearances in all competitions, including 17 outings in France's top flight.