The Colombian has been linked with a move away from the club and if he leaves Marca report that they will go for the Liverpool forward.
They may have an advantage too if they are able to offer Suarez Champions League football, and Liverpool fail to make it to the competition.
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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.