The two sides met in the Champions League last 16 this week, with Klopp’s side going through after winning 3-1 in Germany on Wednesday.
The former Mainz and Borussia Dortmund boss has made a big impact at Anfield since arriving in 2015, leading the club to the Champions League final last season and a serious stake in the Premier League title race alongside Manchester City this term.
He is also a two-time Bundesliga winner from his time with Dortmund, and Beckenbauer believes he would be a great fit for Bayern.
“Jurgen Klopp at FC Bayern. That would be the highlight," he said in an interview with Sky.
"Jurgen was the one who taught the Germans how to play football quickly."
Klopp has a contract until June 2022 with the Reds and has led them to fourth-place finishes in each of the last two seasons.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.