Bayern hold a slender lead over Borussia Dortmund, as the tightest Bundesliga title race in recent memory heads into its penultimate weekend.
The holders will face RB Leipzig, who are themselves pursuing Champions League football, at Allianz Arena in Munich on Saturday.
Dortmund, who are a point behind in second place, travel to nearby Augsburg a day later as they attempt to end Bayern’s 10-season monopoly on the title.
Bayern’s hierarchy reacted to their troubles this season by sacking Julian Nagelsmann and replacing him with Thomas Tuchel last month.
The early part of Tuchel’s reign has been notable for the amount of time on the bench endured by club stalwart Muller.
Recent weeks have seen speculation the 33-year-old forward could seek a move away from the club at the end of the season.
But Matthaus, a former playmaker for both Bayern and Germany, says he cannot envisage one of the club’s great players ever moving away.
“I can’t believe Muller would leave Bayern Munich because Muller is Bayern Munich,” Matthaus said.
“I cannot see him in another shirt. I cannot see him in another place. He is not only a footballer, he is an ambassador, he is the face, he is the press officer, he is making messages, he is making us talk about football.
“The fans love him, and I cannot see him in another team. I can’t see him at Real Madrid. He is not a Real Madrid player, he is a Bayern Munich player.
“If he is not a Bayern Munich player, nobody else is a Bayern Munich player.
“He will stay at Bayern Munich till the end of his career and later he will get a good position in the club, maybe like [former goalkeeper now club chief executive] Oliver Kahn or [ex-player and chairman] Karl-Heinz Rummenigge before.”
At the start of this year, Muller went back on his decision to retire from international football and Matthaus believes his club career has some way to run, too.
“He is not running away because he is sitting sometimes on the bench,” said Matthaus, who captained West Germany to the title in the 1990 World Cup.
“He would like to show everybody he has to play. He has to play because he is not only someone who is a good player but someone who cares about the game, and organises on the field.
“I think a coach should be happy to have on the field a player like Thomas Muller.”