Karius, who arrived at Liverpool in the same 2016 summer transfer window as Mane, believes such a superstar signing is great for German football.
"It would be a crazy transfer for Bayern, because he's one of the top players at Liverpool," the goalkeeper told beIN SPORTS.
"If Bayern Munich manages to sign someone like him, then you can only congratulate them and the Bundesliga too. It would be another star in the league, so I would be very happy for the Bundesliga. Sadio Mane is very reserved, very down to earth.
"He also speaks a bit of German from his time in [RB] Salzburg. I've always got along very well with him, actually everyone. Should he come to Germany, he won't have any problems adapting."
Of his own plans, Karius also said: "There were ups and downs. It's part of the game, that's football, but I've developed as a person.
“I'll take my determination with me to my next job. It's about having a good feeling. The club can be in Germany, but also abroad. I just have to feel that the chemistry with those responsible is right, that they have a good feeling about me, and I have a good feeling with them."