The Mirror reports that a move to the Hammers for Downing could be sorted in the next few days.
The 29-year-old turned down a move to the Hammers earlier this summer, but the London side have come back in and the winger is now ready to leave Anfield.
Downing has failed to make the expected impact at Anfield since joining Liverpool from Aston Villa in a £20million deal just two years ago.
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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.