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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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.