Cole's contract at Upton Park expires at the end of the season and West Ham are ready to sell him in January rather than seeing him leave on a free in the summer.
West Ham indicated they were ready to offer Cole a new contract at the start of the season, but the player and his representatives have heard nothing since from the Hammers' hierarchy.
Sam Allardyce has already brought in two strikers on loan this month in Marouane Chamakh and Wellington Paulista and, with Andy Carroll set to return from injury, Cole could find himself down the pecking order at Upton Park.
The news has alerted a host of clubs to Cole's possible availability this month should the 29-year-old decide to move on.
A number of Premier League clubs are keeping tabs on Cole's situation, while French giants Marseille are thought to be tracking him as a possible replacement for Premier League target Loic Remy.