The report discussing the futures of Payet at Florian Thauvin claims the Hammers have managed to convince Marseille to accept a £12 million offer.
The future of the player would therefore rest with Payet himself, who held talks with the Ligue 1 side over extending his contract.
Always reported to be available at the right price despite West Ham's clear intent to sign him, the issue has been quite what the fee would be and whether the Hammers would pay up.
Why fans should be cautious
French newspaper L'Equipe also reported the same news, but suggested Marseille may still not be swayed to lose a player who was integral to their success last season, providing 16 assists.
GetFootballNews France reported late last night that a new report will be published in Wednesday's L'Equipe, confirming intensifying interest from West Ham, but insistent no deal is agreed.
According to tomorrow's L'Équipe, West Ham United are trying very hard to close a deal for Dimitri Payet by the end of the week.— Get French Football (@GFN_France) June 23, 2015
The size of West Ham's new offer is making Vincent Labrune consider selling. Contract extension talks today not especially positive either.— Get French Football (@GFN_France) June 23, 2015
Their latest update is perhaps encouraging for West Ham fans that they are close to signing Payet, but opposing the report in The Mail, it may not be quite there just yet.