England goalkeeper is likely to be in demand with a host of Premier League clubs looking to sign him on a free transfer.
Robert Green to leave West Ham after failing to agree new deal
The 32-year-old is out of contract at the end of June and has not agreed new terms despite the club's return to the top flight of English football.
Green - currently on duty with the England Euro 2012 squad - spent six years at the Boleyn Ground and is unlikely to be short of suitors with London clubs QPR and Tottenham having been linked with a move for the goalkeeper, along with West Brom and Spanish side Malaga.
Gold wrote on Twitter: "Robert Green is a free agent he has chosen to move on. Matthew Upson did the same thing.
"Nobody wants Rob to leave but nothing is for ever, he must do what is best for him and we must do what is best for us."
Green was an unused substitute as England beat Belgium 1-0 at Wembley on Saturday in their final warm-up ahead of Euro 2012.
He joined the Hammers from Norwich for £2million (AED11m) in 2006 and made 241 appearances.
West Ham manager Sam Allardyce has lined up Bolton's Jussi Jaaskelainen as Green's replacement - with the 37-year-old, who is also out of contract, reportedly set to sign next week subject to a medical.
Jaaskelainen will compete with Stephen Henderson, whose loan move from Portsmouth became permanent last month, to be the club's number one next season.
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