Carlton Cole is undergoing a medical with a view to signing on a short-term contract.
It comes after the Hammers missed out on three international strikers on transfer deadline day.
A West Ham statement on Tuesday read: "Despite the board and manager deciding to do their business early on in the window to avoid last-minute panic buys - resulting in the successful signings of Andy Carroll, Stewart Downing, Razvan Rat and Adrian - joint-chairman David Sullivan and manager Sam Allardyce did spend all night on Monday trying to sign one of three international strikers, but all opted for the lure of European football instead.
'"Importantly, the board also turned down bids for several first-team players in the last week of the window as they are determined to give the squad the best chance possible of bettering last season's tenth-placed Premier League finish."
Cole who also had a spell at Chelsea made 237 appearances for the Hammers over seven years, scoring 59 goals.
Manager Sam Allardyce said at the time of Cole's release in late May: "Carlton's need at his age is to be playing football as often as he can. We felt it better he found pastures new.
Cole scored the opening goal in West Ham's Championship play-off final victory over Blackpool in 2012.
Despite the fact the transfer window is now closed, clubs are still permitted to sign free agents.
West Ham made four senior summer signings in striker Andy Carroll and winger Stewart Downing from Liverpool, left-back Razvan Rat from Shakhtar Donetsk and goalkeeper Adrian from Betis
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