New West Ham owner Eggert Magnusson is to discuss the possible signing of Shaun Wright-Phillips with Chelsea chief executive Peter Kenyon.
Chelsea have hinted they will look seriously at West Ham's offer
"I know Peter Kenyon well and I think we will sit down and try to find the right fee, whatever that might be," Magnusson told BBC Five Live.
"He has not been playing regularly at Chelsea, but he's a good player and he has great possibilities to do well."
Chelsea bought Wright-Phillips, 25, for £21m from Manchester City in July 2005.
West Ham are thought to be willing to pay £10m.
On Saturday West Ham boss Alan Pardew said he was unhappy Chelsea had made public on Friday the Hammers interest in the winger.
"We made an enquiry and I'm a bit disappointed Chelsea have released that," he said.
"On our side, we like to look at market and now and again make a phone call now and again, but there was no bid."
Kenyon has said Chelsea would consider any serious offer for Wright-Phillips.
"We're not looking to sell our players but if we get an offer we'll have to look at it on a serious basis," said Chelsea's chief executive.
606 DEBATE: Your thoughts on West Ham's offer
England international Wright-Phillips has made only 12 league starts for Jose Mourinho's side since his arrival at Stamford Bridge, although he has come off the bench on 23 occasions.
The stepson of ex-England striker Ian Wright is yet to score a goal for the Premiership champions.
West Ham will have money to spend in the January transfer window following the takeover of the club by Icelanders Magnusson and Bjorgolfur Gudmundsson.