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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Who of Europe’s top strikers will move to England this summer?
After a dreadful start to their Bundesliga campaign, Borussia Dortmund appear to have weathered the storm after going five matches without defeat.