Kane is being linked with a return to the Premier League after it broke this week that his contract carries a clause which will allow him to leave for a set price of €60m.
The England captain struck twice on Friday in victory over Hoffenheim to become the fastest at Bayern to reach 100 goals.
"Buyout clause or not. It is not a mandatory clause. He can stay at Bayern. Kane is in very good hands in Munich. He feels very comfortable there," Matthaus told Sport1.
"He has been Germany's top scorer twice and is on his way to his third Bundesliga title. He is winning titles with Bayern, something he didn't do with Tottenham. I don't think he could feel more comfortable anywhere else than at FC Bayern."
Matthäus was also asked if Kane is the best striker in the world.
"Yes. Especially when you look at the goals: He scores everywhere in every competition. He is not only someone who scores goals, but also provides assists. And what I like about an attacking player is when he contributes to the defense - Harry Kane does that brilliantly."