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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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.