West Ham co-owner David Gold says the club will be unable to retain the services of Matthew Upson if an offer of £6 million is received for the England defender.
Upson's current contract expires at the end of the season and the club are concerned that he could leave Upton Park on a free transfer next June.
While talks continue in an effort to tie Upson to a new deal, Gold does concede that the club could be forced into selling the 31-year-old before the transfer window closes on August 31.
"We want to keep Matt here, but at the same time we know we may have to sell him if he tells us he doesn't want to stay," Gold told the Daily Star.
"We don't want to let him leave the club for nothing. It's a difficult balancing act and a dilemma for us. If someone came in and bid £6 million or £7 million for him, we would have to sell.
"We will do everything in our power to keep hold of Matt Upson - as we will do with all our best players. We want to see Upson end his career with West Ham. We want to sit down and talk to him about a new contract - and quickly - because we are in a tricky situation."
However, West Ham are more confident of keeping hold of captain Scott Parker and expect the midfielder to sign a new contract at Upton Park, despite interest from Tottenham over the summer.
"We are hopeful Scott will sign a new contract and talks are ongoing," Gold said. "We know he is very happy at the club."
Striker Carlton Cole is also adamant that he will be staying at the club this summer. The England international has been linked with a move to Stoke City.
"I've never been happier than where I am," Cole said. "It'd take an awful lot for me to move away. I see my future here at Upton Park, nowhere else.
"I'll never forget West Ham were the club who gave me my big break in the Premier League. I want to repay that faith they had in me. I want to be around to correct last season, we didn't have the best. There's been talk about other clubs but nothing is worrying me, I am totally focused on West Ham."