Hamann has told Kane to put the team first, instead of chasing individual accolades.
He continued: "These personal records - that may be important for him - but it shouldn't really matter. Team success is the focus. And as I said: He was back, then Stuttgart. He played at 35 degrees for 90 minutes and then went out in Madrid in the 80th three days later. Such a situation must not happen again."
While Hamann may appear to have his glass half-empty, Lothar Matthaus, another former Bayern icon, believes they have the talent to win a historic treble, with Kane at the forefront.
He said: "Bayern is the team that is currently performing best in Europe. Not just because of two games, but actually over the entire year. That's why Bayern is also the favourite against Real Madrid for me.
"I believe Bayern can not only win the title, but even the treble this year. The chances are definitely there, and the quality in the team is excellent at both ends of the pitch."