The 29-year-old, who spent two seasons at the Stade Veledrome before making the move to East London in 2015, is said to be agitated with the Hammers' failure to build on last term.
Payet has himself failed to live up to the burgeoning expectations placed on his shoulders, only intensified by an impressive Euro 2016 campaign with home nation France that saw him linked with a number of European heavyweights.
According to Bleacher Report, the form of both West Ham and Payet has given Marseille chiefs hope of re-signing their former player, and they will test the water by making an offer during the January transfer window.
It is claimed that United would be tempted to cash in should a bid of £35m be made, knowing that they will likely see the attacking midfielder's valuation decrease come the summer.
Payet has also previously represented AS Excelsior, Nantes, Saint-Etienne and Lille.