Rumours in both Germany and France are rife about Bayern poaching Mane with his contract expiring next summer, and Klopp has hinted at parallels with Mario Gotze.
Gotze was one of Klopp's key men during his back-to-back title wins with Borussia Dortmund, but a move to Bayern was announced days before the German sides faced off in the 2013 Champions League final.
Dortmund eventually lost the Wembley clash 2-1 in Gotze's final game, and Bayern later added Robert Lewandowski the following summer.
Klopp was asked about reports linking his star Senegalese forward with Bavaria ahead of the Champions League final against Real Madrid, and failed to dismiss them.
"Sadio is in the shape of his life," he said. "For sure he's in brilliant shape and it's a joy to watch him at the moment in training and in the games.
"We ask him a lot, football asks him a lot this year, incredible long season, lot of finals and these kind of things so for sure it's one of the most successful so far for him and for us."
Klopp recently revealed he snubbed Bayern's advances on multiple occasions during his management career, and has now questioned 'what he did' to upset the Bundesliga winners.
He said: "The Bayern Munich rumours I couldn't care less in the moment, we are all fully focussed on the game, Sadio is completely focused on the game.
"He knows how important it is to him, how important it is to us, so no concerns, completely normal.
"It's not the first time in my career that before decisive games Bayern Munich rumours coming up, don't know why, exactly what I did, why that happens, but no problem at all."
French outlet L'Equipe say Bayern could sign Mane for as little as £25million, due to his expiring contract and Robert Lewandowski's impending departure.
Reports in Germany are claiming similar, with Bayern's sporting director Hasan Salihamidzic making Mane his top priority this summer.
Klopp was again asked about the news in his pre-match press conference, and didn't offer any reassurances.
"We started already to talk about Sadio right? And this is the wrong moment to speak about that," he explained.
"I said it before, wherever Sadio will play next season he will be a big player, definitely."
Mane had previously kicked off doubts over his future by saying he would reveal his decision after the final, and has since offered a further update.
The 30-year-old said: "Honestly, the answer I can give you now is I feel very good, and I am fully focused on Saturday's game.
"That is the answer I must give before the final. But come back to me on Saturday and I will give you the best answer you want to hear, for sure. It's special.
"I will give you all you want to hear then. For now, let's go win it because I have no time for other things.
"I will do everything possible to win it because it is my and all the boys' biggest dream, then I will give you the answers."