The report states that Klopp is determined to improve the quality available to him in midfield and has set his sights on the Germany international.
Gundogan has been linked with a move to Liverpool since the appointment of Klopp. The charismatic manager managed Gundogan during his period at Dortmund.
However the Red’s may find it difficult to sign the 25-year-old after Dortmund have rejected a €30 million bid from Juventus for Gundogan.
Gundogan played the full 90 minutes during Borussia Dortmund’s disappointing 2-1 defeat at the hands of FC Koln in the Bundesliga. Dortmund sit in second place in the league with 38 points in 17 games.
The deep-lying playmaker has five assists and two goals for Dortmund in 28 appearances this season.