Klopp's current contract runs to 2024.
Hamann told BILD: “It is astonishing that Jürgen Klopp has already been a coach at Liverpool for five years.
“But when you are successful, time goes by faster.
“Since the Champions League victory against Tottenham in 2019 and the first title this summer for Liverpool after 30 years, this coach is a living legend.
“I would wish for Liverpool that he would still be the coach in 2025.
“But either Klopp will be lying on the beach, or he will be the coach of the German national team."