The Senegal international met the German when he was Borussia Dortmund boss and Klopp admits not signing the then Red Bull Salzburg player was a mistake for which he would have "punched himself".
Mane moved on to Southampton but when the chance arose to sign him Klopp did not make a similar error, having tracked the pacy attacker since the 2012 Olympics.
"I remember everything about it, because it was a meeting to talk about football and how he wanted to play and how he wanted me to be part of his team," Mane told liverpoolfc.com of his 2014 meeting with Klopp.
"I think it's part of football, that these things can happen. After that I never stopped working like I did before.
"I gave my best all the time and finally, we work together.
"We didn't speak (when he signed for Liverpool) about what happened before because we know it's part of football and it can happen.
"It wasn't his fault, or my fault, or the clubs' fault.
"When he called me to come here, it was the right time, the right coach and the right time to come to Liverpool.
"The next thing now is to play in the Champions League with Liverpool and win trophies with Senegal, and why not win many, many trophies with my club, as well?"