The Romania international's contract at Shakhtar Donetsk is expiring and the left-back is believed to have been a target for the Hammers since the January transfer window.
Agent Florin Manea claims that a deal could be concluded as soon as Monday with Sam Allardyce a big fan of the 31-year-old defender.
"I am with Razvan in England, we are negotiating with the West Ham officials," Marin told Sport in Romania.
"We will probably sign the contract on Monday. The trainer has put him on the top of the wishlist and the owner has approved the move."
West Ham have reportedly fought off interest from Marseille by bettering the deal that the French club could offer the player.