Spanish outlet El Desmarque claims that the Reds are in negotiations with Sevilla for the 26-year-old Diego Carlos, who has caught the eye with a series of impressive performances this season, and are willing to meet his £65m release clause.
The Brazilian joined Sevilla from Ligue 1 side Nantes for just £13.5m in the summer but his value has significantly increased due to his form.
The report claims that Real Madrid are also interested in Carlos and see him as the long-term replacement for club legend Sergio Ramos.
Carlos has played all but 15 minutes of Sevilla’s La Liga campaign this season, helping them to third place in the table.
As well as bringing new faces into the club, Kloop is also desperate to keep hold of Adam Lallana for another season with the midfielder’s contract expiring in the summer.
The England international can sign a pre-contract on Wednesday with a club abroad.
A queue is forming for Lallana’s services according to the Telegraph and Klopp knows he is too good to be a squad player.
Paris Saint Germain could be one of the suitors to sign Lallana next summer in a shock move.
The 31-year-old has also recently been linked with a move to China or the United States.