Diame is available for £3.5 million due to a release clause in his contract.
Arsenal and Everton are among the other teams in for the player, who joined West Ham from Wigan in the summer.
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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.