Klopp guided Dortmund to consecutive German top-flight titles during his time in charge, as well as two DFL-Supercups and a DFB-Pokal trophy.
And while he is yet to taste silverware with Liverpool, he has been in two major finals during his 18 months in charge of the Anfield club, losing to Manchester City in the League Cup and then Sevilla in the Europa League.
And Hitzfeld, who won seven Bundesliga titles as a manager between Dortmund and Bayern, would like to see Klopp follow in his footsteps to Bavaria.
"Jürgen Klopp always belongs among the candidates at Bayern," Hitzfeld told t-online.de. "He knows the Bundesliga, became German champion and won the trophy. I think and expect him to be a coach at FC Bayern."
Hitzfeld has also tipped Klopp to secure the Premier League title at Liverpool and is proud of the way he is leading the way for German managers abroad.
"Jürgen Klopp is one of the top coaches, but he has not won any major international titles compared to the others," he added.
"He will be an English champion sooner or later, of which I am firmly convinced. He is building something in Liverpool, is a motivator, and is a fantastic advert for German trainers. To get through in England is not easy - he did it."