The England striker, who is also reported to be linked with a move to Aston Villa has been in good recent form for West Ham. A reported £4 million bid is being considered by Fulham who are looking at options should they be forced to sell Bobby Zamora in January.
West Ham will be reluctant to sell Cole with mounting injury concerns to their strike-force threatening to derail their bid for promotion back into the Premier League. The Hammers have had bids for Jordan Rhodes and Peter Whittingham rejected which will likely slow or halt entirely any transfer process with regard to Cole.
Fulham manager Martin Jol is known to admire Cole and has attempted to sign him in the past when the Dutchman managed Spurs.