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The forward was something of a legend at Anfield, scoring 120 goals in 269 games and helped his side win the Premier League and Champions League.
But this summer, Mane decided to call it quits and joined the German champions for a fee that could rise to £35m.
Speaking to ViaPlay football, Klopp spoke highly of his former player: “Sadio told me and his agent told me that he was looking for a new challenge."
"And if that happens early enough, like it was in this case, and if that happens in the right way and the player and the agent are working, and the new club where they want to go is ready for negotiations, then it should be like it was now."
"Then you say 'thank you' with the biggest respect ever, I couldn't have more respect for Sadio, what a player he is and I wish him the best - and he will play for ages, he can play until 38 or 39 with his body, it's absolutely crazy."
That Sadio informed his coach of his intention to depart so early on allowed Liverpool to find a suitable replacement.
The Reds did just that, and brought in Uruguayan star Darwin Nunez from Benfica for a fee of up to £85M
The Liverpool manager closed by stating: "Bayern have got a really good player but we had him for six years, so that's fine."
"I'm really fine with the situation. We will miss him from a sports point of view and as a person as well. But I am fine because that's how life is."
Klopp's side will be in action tomorrow evening against RB Slazburg in their fourth pre-season outing of the summer.
Kick Off is at 7pm BST, and the game will take place at the Red Bull Arena