West Ham co-chairman David Gold says there is an open invitation for David Beckham to join the club.
England coach Fabio Capello has said he will not pick the 35-year-old for another competitive international.
But Gold would like to take the former England captain, who is currently with Los Angeles Galaxy, on loan as a player or for him to be a club ambassador.
"He's still a great player and it would be a fantastic statement if he came to West Ham," Gold told BBC Sport.
Capello revealed in a TV interview before England's 2-1 friendly win over Hungary that he was ready to cast Beckham aside, saying the former Manchester United star was "probably a little too old".
Beckham speaking in July
But Gold believes Beckham could still be a force at international level.
"I'm a little disappointed with what happened to David on Wednesday night," he said. "It's not like he had a bad game, or he's declined as a player all of a sudden. He's just been dropped for his age.
"If it is truly the end of his international career, I think it's a bit of a damp squib."
Beckham, who is recovering from an Achilles tendon injury which ruled him out of the World Cup, has 115 England caps - more than any other outfield player.
In July, a spokesman for the player, who was born in Leytonstone, east London, said there had been no talks with West Ham.
"While it's flattering, there has been no contact or offer from West Ham. David has no interest in leaving," he said.
Gold concedes there have been no direct talks with Beckham, but said an approach to his representatives had been made.
There's a natural fit for us, were it to suit David Beckham
David Gold, West Ham co-chairman
"We showed interest at the end of the season and asked would he come and join us, maybe just for half a season on loan," said Gold, who took over West Ham with business partner David Sullivan in January.
"Sadly, his commitments are such that this is probably not going to happen now. The January transfer window doesn't look possible, but we still have an open invitation to David to join us.
"Our belief is that he is still a great player and it would be a fantastic statement if he came to West Ham. He's an East End boy and it would be a fitting end to his career."
The Hammers believe Beckham could help as they seek to move from Upton Park to the new Olympic Stadium at Stratford after the 2012 Games.
"We also had in mind his value as an ambassador to to help us with securing the Olympic Stadium," said Gold, who grew up close to West Ham's current ground.
"He was an ambassador for the 2012 bid and is doing the same for the 2018 World Cup.
"I see the value in David Beckham after his playing career is over. If he wasn't an east London boy, I wouldn't have the same enthusiasm.
"I played over at Leyton a number of times as a lad in the Isthmian League and it's right in our territory. You can probably see David's old house from the new stadium."
Capello said Beckham could play once more for England at Wembley so fans could pay tribute to the ex-skipper.
But Beckham's agent released a statement confirming the player's desire to carry on playing for England.
It read: "For your information, there has been no discussion of retirement. He will always be available for his country, when fit and if needed he will be there."
Beckham was back in full training with United States side LA Galaxy on Wednesday and is hoping to return to Major League Soccer (MLS) action in September.
However, Italian club AC Milan have said he he is unlikely to have a third loan spell there after the MLS season ends in November.
"There's a natural fit for us, were it to suit David Beckham," added Gold.
"But the man's a superstar. Who knows what he's going to do? He could go into films and you'd never see him again in football.
"Every day that passes makes it a less likely option that he would consider coming to us as a player."
Beckham has previously said he is proud of his East End roots, although he was temporarily a hate figure among some West Ham fans after he was sent off for England against Argentina at the 1998 World Cup.
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