United reportedly bid £85m for the Germany international in the summer of 2015 but a transfer failed to materialize, and Muller says though he gave it his consideration, the support Bayern showed made his mind up to stay.
“There was a stage when the subject [a move to United] arose two years ago when I considered it, but then the club immediately backed me and I was told I belong here,” Muller told Kicker.
“I didn’t have to think about it a great deal after Bayern said we are counting on you and that you are an important man for us.”
“Of course, it’s possible [to leave]. When my time is up, it’s up. [Bastian] Schweinsteiger was here for over 10 years and now he’s been gone for over two years and another player is here instead.
“It will be exactly the same with me. If I drop dead tomorrow, there will be a funeral, yet on Friday, 11 players will still be out on the pitch. That’s life.”
Muller scored just five Bundesliga goals last season and has regularly started on the substitutes bench, with manager Carlo Ancelotti preferring to start Spanish attacking midfielder Thiago Alcantara behind Robert Lewandowski.
The situation led Muller to speak out in August and tell ARD: “I don’t know exactly which qualities the coach wants to see, but mine seem not to be 100 per cent in demand.”
Muller was subsequently criticised for the comments by Bayern chief executive Karl-Heinz Rummenigge, but the 27-year-old academy product says he is committed to the Bundesliga champions, while also leaving the door slightly ajar for a potential exit at some point.
“At the moment, I don’t think it’s going to happen because I am very happy here,” Muller added to Kicker. “However, I’m not saying that somewhere different in the world definitely wouldn’t be my thing either.
“If life takes you somewhere else then I would make myself at home there as well. I would follow the same principle as here, enjoying as many good things as possible every day.”