Cole has a clause written into his contract which ensures his wage will be cut in half after the club failed to retain their place in the top flight when losing 3-2 to Wigan Athletic at the weekend.
David Sullivan said the England internationals would be allowed to leave the Hammers and join a Premier League clubs, but Cole could be a huge 'white elephant' because he has always insisted he wants to stay in the south.
ager Alan Pardew signed Cole for West Ham in 2006, views the player as a possible replacement for Andy Carroll following his £35 million move to Liverpool in January.
Cole was valued at £15 million by West Ham 12 months ago but the club are now likely to accept around half of that.