The former England captain is set to leave Los Angeles Galaxy next month and David Gold is keen to hand the 37-year-old a return to the Premier League with the Hammers
The 37-year-old will play his last match for the club on December 1 and has been the subject of much speculation as PSG and Melbourne Heart reportedly consider a deal for the ex-England captain.
But Gold feels that Beckham would favour a return to Premier League football and move back to the east end of London, where he grew up.
"He was an ambassador for the London 2012 bid and it would be a fantastic statement if he came to us," Gold told reporters.
"He's an East End boy and it would be a fitting end to his career. We've also been mindful of his value as an ambassador to help us secure the Olympic Stadium."