Gotze burst onto the stage as a teenager with Dortmund under Klopp's wing in a memorable BVB team that beat out Bayern Munich to the 2010-11 and 2011-12 Bundesliga titles.
A move to Bayern Munich and the winning goal in the 2014 World Cup final for Germany then beckoned for the forward, before he returned to Signal Iduna Park in July 2016.
The 26-year-old has confirmed he had the opportunity to seal a reunion with his old boss at Anfield upon leaving Bayern.
"I decided to leave Bayern and Jurgen Klopp was interested in getting me to Liverpool. And I was also interested in working with him again," Gotze said in the DAZN documentary 'Being Mario Gotze'.
"It's still existing. He is a world-class coach and that's why it's always an option. I decided to join Borussia Dortmund, but it was not a decision against Liverpool or Jurgen Klopp. But on the contrary."
Liverpool boss Klopp added that Gotze's Dortmund exit in 2013 was one of the biggest shocks of his managerial career, having received the news hours after a crunch Champions League clash.
"I did not expect it at all. One day after knocking out Malaga [in the Champions League quarter-finals], one of the biggest games of all our careers, Michael Zorc said to me: 'We have to talk for a minute. Mario is going to Bayern.'," Klopp recalled to DAZN.
"I turned around, walked out of the office, drove home, got into bed. We had a movie premiere of (German actor) Wotan Wilke-Möhring in the evening.
"My wife was already done and stood there to go. I just said: 'Tonight nothing is possible.' It's just football, but the timing really hit me.
"After the highest high against Malaga and qualifying for the semi-finals of the Champions League I was not prepared for that."