West Ham co-owner David Sullivan has confirmed he would 'love' to sign David Beckham, but admits Joe Cole has spurned a move.
The Hammers have suffered well-documented financial difficulties of late and are still in the process of cutting costs.
They would, however, be prepared to splash out on Beckham, who would command a substantial salary.
The former England captain is currently nursing an Achilles injury which has brought an end to his World Cup dream.
He is also still on the books of MLS outfit Los Angeles Galaxy, who he joined in 2007.
Beckham has returned to Europe in each of the past two seasons, though, taking in loan spells at Italian giants AC Milan once the American season has come to a close.
Sullivan is hoping the former Manchester United ace can now be persuaded to have another shot at the Premier League, with the Hammers keen to bring him back to his East End roots.
"I'd love David Beckham," Sullivan told the Daily Mail.
"He has massive cult status in East London and still has a house near Bishop's Stortford, not far from our training ground. He's from Chingford, which is our heartland. We are the club of east London and Essex.
"If AC Milan didn't want him in January and if he still wanted to do it, I'd love to have him. He seems a remarkable professional."
While Beckham remains a realistic proposition for West Ham, Sullivan has revealed that Joe Cole will not be heading back to Upton Park.
The England international is set to become a free agent this summer, with his contract at Chelsea running down.
Cole began his career with the Hammers, making over 100 appearances for the club before crossing London to Stamford Bridge in 2003.
Sullivan had hoped the 28-year-old would be willing to consider an emotional return to where it all began for him, but admits there is no chance of a deal being struck.
He said: "We've asked Joe to name a price but he said no.
"We're fishing high and wide and we'll land a few. We're probably looking at 50 players and we might sign four or five. A lot depends on who goes."