Klopp is keen on being reunited with his former pupil who he trained and developed during his time at Dortmund.
Gundogan has another 12 months on his current contract but has yet to sign an extension and is unlikely to do so if reports from Germany are to be believed.
Liverpool could however, face competition from Premier League rivals Manchester City who are also interested in the Germany international of Turkish origin.
In fact City sporting director Txiki Begiristain has already met with Gundogan’s uncle and agent Ilhan Gundogan regarding a summer deal.
Klopp does have an advantage over City in terms of having already worked with the 24-year-old midfielder but City are likely to be be able to offer a more attractive financial incentive.
The Reds manager is also reported to be keen on Empoli’s Piotr Zielinski and Borussia Monchengladbach’s Granit Xhaka.