The Ligue 1 side have been heavily tipped as favourites to sign the outcast, even as West Ham remain adamant that they “won’t be bullied into agreeing anything”.
That is bad news for Marseille, with the Stade Velodrome outfit having already seen two bids to take Payet back rebuffed.
Goal understands that West Ham are looking to bring in around £30 to 35 million from any deal that would see a prized asset move on after just 18 months in east London.
They have now made it clear that there is no room for negotiation within that valuation, with any interested parties warned to look elsewhere if they are not prepared to pay the going rate.
Hammers Vice-chairwoman Brady wrote in a column for The Sun: “If Marseille want a bargain they ought to try Roman Road market.
“They should know that Dimitri Payet, skilled enough to play for Real Madrid as well as West Ham, isn’t going cheap, should we decide he can leave at all.
“Chelsea are in the same boat [with Diego Costa] and holding firm like us.
“My chairmen and the manager keep repeating they want to keep Payet.
“I can assure you they won’t be bullied into agreeing anything that is not in the best interests of WHU.”
West Ham boss Slaven Bilic has aired his disappointment at seeing Payet rule himself out of contention for future fixtures, but has also hinted that a compromise could be reached that sees a wantaway star stay put.
He said: "Payet's departure is not inevitable.
"I like to solve situations in-house to protect the team.”
The Hammers will, however, be without Payet again when they face Middlesbrough in the Premier League on Saturday, although his absence did not hold them back last time out as they crushed capital rivals Crystal Palace 3-0 at London Stadium.