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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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.