The midfielder played under Klopp at Borussia Dortmund, but the Germany international told Fantasy PL (h/t Josh Challies of the Liverpool Echo) he was keen to have a new football experience when he moved to England in 2016:
"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.
"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."
Gundogan earned an impressive reputation with BVB, winning the 2011-12 Bundesliga title and making the UEFA Champions League final the following year.
Klopp honed his management style for seven years at Signal Iduna Park before exiting Dortmund in 2015. The coach resurfaced at Anfield five months afterwards.
The German would have been perfect for Klopp's needs, and his performances at City indicate he would have been a huge hit on Merseyside playing for his compatriot.
The 29-year-old is a two-time Premier League winner, but it seems he will have to watch his former boss scoop up the title with the Reds. Liverpool have built a 22-point advantage over second-placed City in the title race, and Guardiola's men have been unable to keep up with Klopp's unbeaten exploits this season.