Müller's former teammate Franck Ribery, however, remains hopeful that the 35-year-old will remain at the club.
"Personally, I hope he can stay at Bayern for another year," Ribery told Sport Bild.
“I remember that I signed my last contract very late, in May 2018. It was the same situation.”
Ribery, who went on to play one more season for the Bavarian giants, points out that Müller remains an important member of the squad, even if he rarely starts games.
"Thomas is very important for the dressing room, he has a big influence. He is important whether he plays 90 minutes or five," Ribery said.
“Thomas has done so much for the club, for the city of Munich. If he wants to play another year, then the club should give him this contract.”
Ribery and Müller played together for 11 years.