The Reds are of course looking for a new manager after sacking Brendan Rodgers following the 1-1 draw against Everton in the Merseyside derby at Goodison Park.
Gündoğan is of course familiar with Klopp having played under the stewardship of the German coach during his stint at Dortmund.
“I’ve not had that much contact with him recently, and I’ve not followed much of what has been said, but I think Klopp would be a great fit at many clubs and I believe also at Liverpool,” the Germany player said at a national team press conference (via Thisisanfield).
“Of course it’s something I can see happening. I think Klopp is capable of helping many top clubs in the world.”
Klopp won two Bundesliga titles and finished the 2012-13 Champions League as runners-up during his time in charge of Dortmund.
Gündoğan joins Liverpool star Emre Can in the Germany national team camp ahead of the Euro 2016 qualifier on Thursday against Ireland.