Klopp managed Gundogan at the German club, but the player did not want to join Klopp at Liverpool.
The possibility of a move was present in 2016, but Gundogan says that he turned down Klopp's advances.
"I believe in challenges in life and I always try to challenge myself first of all. I feel like if I don't challenge myself and get out of my comfort zone, I'm not going to change anything and won't improve.," he told FantasyPL.
"So I had a great four years with Jurgen and I love him as a person and a manager but I felt it was time for something else.
"I wanted to leave Dortmund in Dortmund and didn't want to think about the time that I had with him when I was joining a new club.
"That was a bit of the reason why I didn't want to join Liverpool."