Already moves have been made to sign a winger, with Roma's Mohamed Salah the priority.
But, for a variety of reasons, Jurgen Klopp couldn't quite bring a new wide midfielder to Anfield.
Now, as the summer transfer window prepares to swing open, the Reds boss isn't going to make the same mistake twice.
The Bayern Munich winger is keen to make a move this summer having struggled to earn a regular spot under Carlo Ancelotti.
And Bild claim several clubs have been sniffing around including Liverpool and Tottenham.
Juventus, Manchester City, and Manchester United are also mentioned.
However they are looking at alternatives and Costa appears to be one of those.
German publication Bild claim he is on Jurgen Klopp’s radar.
Klopp has already agreed the signing of Dominic Solanke, who will arrive on July 1, but he wants a forward who can go straight into the team.
And Salah and Costa fit the Klopp prototype of fluid players who can play anywhere in the front line.
Costa would cost around £35million - a similar fee to Salah - but Liverpool would face competition from a number of clubs.
The deal to take Salah from Roma is in the works with wages of £90,000 a week said to be agreed, but a an agreement with Roma still to be reached.
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