That's according to football agent Muzzi Ozcan who claimed last night that Payet is geared up for the move and awaiting the two clubs to come to an agreement.
Speaking on his Twitter account the agent, who is an associate of Hammers boss Slaven Bilic and was the first to reveal the Croatian had signed a deal to become the club's new manager, said nearly everything is in place.
"Payet would move to West Ham ... It's all down to two clubs agreeing," he said.
Payet would move to West Ham ... It's all down to two clubs agreeing Good Night— Muzzi Ozcan (@Muzziozcan) June 20, 2015
The signing would be a real coup for the East Londoners and a show of intent in the transfer window as Payet has earned nine full caps for France and is highly rated across Europe.
Just yesterday the likes of the Telegraph claimed West Ham had lodged an increased £14 million bid for a player who had the most assists in the French Ligue 1 last season.
The former Lille attacker has been linked with a move to Chelsea in the past but could now pitch up in East London where he could ironically play under Bilic, who rivalled his Marseille manager Marcelo Bielsa to be Sam Allardyce's successor at West Ham.
Payet, 28, can play as an attacking midfielder in a number 10 role or winger and has a good record of 58 goals in 296 career games so far, including one for France.
The star is quick and blessed with terrific technique and dribbling skills, something that would go down well with West Ham fans who like to see football played a certain way.
Payet would be West Ham's second major signing of the summer after the arrival of Spanish midfielder Pedro Obiang from Sampdoria.
Just last week former Hammers favourite Dean Ashton said his old club had been missing a midfielder with skill and guile for nearly a decade.
Hammers boss Bilic seemingly he agrees as he reportedly looks to push through a move for a player that has both in abundance.