The Brazilian forward has been targeted as the Anfield outfit brace themselves for Luis Suarez’s departure.
Costa struck 20 goals in 44 games alongside Radamel Falcao last season.
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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.