The World Cup winner had the chance to explore that option back in 2016.
As he pushed for a move away from Bayern Munich, various discussions were held regarding his next move.
Gotze eventually decided to return to Dortmund, but only after holding talks with Klopp – with Liverpool credited with an interest at that time.
That could be rekindled in the near future, with the 26-year-old having rediscovered his form of late to enhance his reputation once more.
He is only under contract in Germany until the summer of 2020 and admits to still being in constant contact with a manager at Anfield who gave him his big break.
Gotze told Bild of transfer talks: "He [Klopp] knew that I wanted to leave Bayern. Of course, we talked. He knows me very well and that I am always looking for new challenges.
"I often speak to Klopp. He brought me to the first team when I was 17 and he made it all possible. We never stopped talking."
Klopp is currently looking to lead Liverpool to a first title triumph in 29 years, having previously tasted domestic dominance with Dortmund in the Bundesliga.
Gotze enjoyed working under a fellow countryman, as well as relishing the opportunity to learn from Pep Guardiola during the Catalan’s spell at Bayern.
Two proven winners are now competing for Premier League glory, with both considered to be among the very best in the business.
Gotze, as a man well placed to pass comment on the qualities of Klopp and Guardiola, said of two rival tacticians: "They are difficult to compare because they pursue different philosophies. The fact is that both are extremely successful.
"I am grateful to have worked with two such outstanding coaches. I watch the games of both teams as often as possible, the title fight in the Premier League is extremely exciting."
Gotze is currently chasing down another title of his own, with Dortmund readying themselves for a potentially decisive Der Klassiker clash with old adversaries Bayern on Saturday.