The Chelsea forward is out of favour at Stamford Bridge, and Brendan Rodgers is keen to bolster his forward line at Anfield.
The player could cost Liverpool £12 million as they look to give Luis Suarez support up front.
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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.