The Germany international was a target for Klopp during his time at Schalke 04, where he caught the eye with a string of dazzling displays in the Bundesliga.
Sane did not consider quitting the Veltins-Arena to join Borussia Dortmund as a youngster, though, and he also rejected advances from Liverpool ahead of agreeing to sign for Man City 18 months ago.
"Yes, I was also talking with [Liverpool]," he told The Guardian. "Jurgen was calling me too, talking to me. That was before I joined City.
"He did a good job at [Borussia] Dortmund – I met him when he was there. He's a good guy, nice guy – honest. He [has] worked well with Liverpool.
"There was a time when I was still in the academy that I could have gone there from Schalke [to Dortmund] but there were no thoughts at all to move to a rival."
Sane is a part of the City squad that will travel to Anfield on Sunday afternoon, as the Citizens look to keep their unbeaten domestic run going.