The Hammers have rejected bids from Fulham, Birmingham and Stoke for Cole.
Cole joined West Ham from Chelsea for £1million in the summer of 2006 and the striker has become a key player at the club.
Reports suggest Arsenal and Aston Villa are also interested in the striker.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.