That's according to Calciomercato.com (h/t Metro's George Bellshaw), which claimed that the likes of Manchester United and Juventus are also after the passing wizard, but that Klopp hopes to be reunited with Gundogan next summer.
The 25-year-old's contract expires at the end of next season, and he opened the door to a move during a recent interview with Bild (via ESPN FC's David Amoyal):
Gundogan and Dortmund have an odd relationship, and the Germany international always appears to be on his way out of the club. In 2015, the club officially announced he wouldn't be renewing his contract and would leave the club―only for Gundogan to sign less than three months later, as explained by Bleacher Report's Nick Akerman.
At the time, Gundogan was only just returning from a serious back injury that kept him sidelined for a year and saw him miss out on the 2014 FIFA World Cup. The injury likely played a big role in his decision to stay at Signal Iduna Park, as other clubs were unlikely to offer him favourable contract terms.
He's since worked his way back to his best form, however, and once again looks like the pass maestro fans have come to know and love. Here's a look at some of his highlights from the past few months:
A crafty playmaker with almost limitless range, Gundogan is frequently compared to former Barcelona star Xavi. He glides in and out of pockets of space and plays one of the prettiest long balls in the Bundesliga, but he also feels comfortable close to the opponents' box.
Gundogan isn't an advanced playmaker like Arsenal's Mesut Ozil, and his contributions often don't make much of an impact on a statistical level. But his smart passing underneath is a key aspect of Dortmund's play, opening up acres of space for his attacking team-mates.
There's little doubt he would be a fantastic signing, and given his link with Klopp, it's easy to see why Liverpool are being touted as a possible destination. Whether Klopp is actually calling Gundogan is unclear at this point, and while it's possible, we won't know for sure until one of the parties confirms or denies these rumours.
Jurgen Klopp Denies Joel Matip Deal
What we do know is Liverpool have not signed Schalke 04 defender Joel Matip to a pre-contract, contrary to some reports that surfaced in the last few days.
David Maddock and Alex Richards of the Daily Mirror previously reported the centre-back had agreed to a deal in principle with Liverpool, which would see him join the club next summer.
According to Goal.com's Melissa Reddy, Klopp has denied those reports, saying, “There’s nothing to say about this, to be honest. I don’t know who spoke about it and said something is fixed. When something is fixed or whatever, you’ll be the first I speak about it with, so there’s nothing else on this.”
Matip has been a key member of Schalke's defence this season but is widely expected to leave Gelsenkirchen at the end of this season. His status as an impending free agent means clubs can sign him to a pre-contract during the January window.
Here's a look at what clubs can expect from the Cameroon international:
The 24-year-old has all of the physical tools to thrive at the position, along with remarkable athleticism and decent passing range. He can struggle with the mental side of the game and lacks the vision and anticipation to be an elite defender but can be very effective when paired with a more experienced partner.
As a free agent, Matip would present tremendous value for the Reds, who have been decimated by injuries this season and have a dire need for depth. He's perhaps not the world-class option the club needs for its long-term plans, although he's still young enough to learn how to become a smarter defender.