After a slow start to life at Signal Iduna Park, Gundogan went on to become a pivotal part of Klopp's Dortmund side, helping them win the Bundesliga in his first season and reach the Champions League final the following year.
Frequent injuries have since impacted the Germany international, but when fit he has continued to be an asset to Pep Guardiola's City, who face Klopp's Liverpool in the Champions League quarter-final.
And that occasion gave Gundogan a good opportunity to look back on his time with Klopp and thank the 50-year-old for his influence.
"I had four fantastic years with Jurgen," Gundogan is quoted as saying by City's official website.
"We won a lot of things together, we lived through many different experiences together, we had our lows, too.
"I came to Dortmund from a relatively small team and I struggled during my first six months to find my place there. I was a bit shy and, to be honest, I wasn't brave enough do certain things.
"But thanks to the help of my team-mates, and with the help of Jurgen and his staff, too, I managed to improve.
"I was finally able to find my way and my place. It was hard, but I learned a lot and I tried to assimilate everything at that point.
"Jurgen played a very important role in all that and I'm very grateful to have played in that team at such a high level for so many years. I learned a lot and I managed to improve my game a lot, too.
Klopp: Why I'm different to 'extraordinary' Guardiola.
The boss has provided a fascinating insight into the differences between his approach and that of the Man City manager: https://t.co/VPGgbQNZ0d pic.twitter.com/JJdJKAK6b6 — Liverpool FC (@LFC) April 2, 2018
"Those days left a mark on my career. Those were my first steps in European football, too, because it was an opportunity that I hadn't had before. So that's another thing I have to thank him for."
City and Liverpool face each other in what promises to be a tantalising tie given the two sides' penchant for attacking football and Gundogan says Guardiola's men will look to learn from their thrilling 4-3 Premier League defeat to the Reds in January.
"Liverpool are still the only team that's been capable of beating us in the Premier League, but we're aware why this happened, although we performed pretty well that day," he added.
"Obviously, going back to Anfield for the first-leg game is a great motivation for us. We'll try to play well and get a good result for the second leg.
"I think we're aware of our strengths and we know what we're capable of. We want to prove that in both games."