Hitzfeld believes Klopp's achievements with the Reds should be heralded, and that he is proving that he is "creating an era in Europe" with the squad he has put together at Anfield.
"Jurgen Klopp has done sensational things," he told t-online.de . "In the Champions League, Liverpool have outgrown themselves. He pushed the team with his enthusiasm. Getting ahead of Manchester City was a bit of a sensation.
"They are also stronger away from home because they can then counter with Sadio Mane, Mohamed Salah and Roberto Firmino.
"Klopp has finally made the breakthrough there. I am even convinced that he will create an era in Europe with Liverpool. He has already proved in Dortmund that he can win titles."
Klopp, who won two Bundesliga titles during his time with BVB, has been linked with Bayern for some time and Hitzfeld thinks he may finally make the move in the next few years.
"I still think he has the skills to be a Bayern coach - and that he will be," he added.
"I also believe that he will eventually become national coach. He is still young and he would be the ideal man for both posts: he is a sympathiser, a motivator and he has contributed a lot to the German football culture.
"Maybe he will be first Bayern and later national team coach - after spending three or four years in Liverpool."