Klopp oversaw Liverpool's superb 3-1 Champions League win at Bayern last night to reach the quarterfinals.
Beckenbauer told Sky Deutschland: "Jürgen Klopp at FC Bayern? It would be the highlight.
"Jürgen was the one who taught the Germans to play football with speed."
Klopp has insisted he's happy at Anfield, where he is contracted until 2022.