United reportedly tabled a £85m (€93.6m, $112m)bid for the forward in the summer of 2015, with then-manager Louis Van Gaal keen to be reunited with Muller, who he had promoted to Bayern's senior squad in the 2009-2010 season.
However, while the 27-year-old was given the opportunity to think about the move, the support he felt from Bayern convinced him to remain in Bavaria instead of moving to the Premier League.
"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 German football magazine 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."
United eventually signed a Bayern Munich player that summer, as Bastian Schweinsteiger swapped the Allianz Arena for Old Trafford and Muller has not ruled out the possibility of emulating his former teammate.
"Of course, it's possible [to leave]," he explained.
"When my time is up, it's up. Schweinsteiger was here for over 10 years and now he's been gone for over two years and another player is here instead.
"At the moment, I don't think it's going to happen because I am very happy here. 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."
Muller scored only nine goals in all competitions last season, as Bayern manager Carlo Ancelotti initially deployed him on the right wing, preferring to play Thiago Alcantara behind Robert Lewandowski.
Muller, who is under contract with Bayern until 2021, was then restored to his favourite second striker role in January but only managed four Bundesliga goals until the end of the season, a paltry return given he had scored 54 times in the previous two campaigns across all competitions.
The Germany international, who started as Bayern suffered a surprise defeat 2-0 away to Hoffenheim on Saturday (10 September), is yet to score this season. Last month, Muller was criticised by Bayern CEO Karl-Heinz Rummenigge as he spoke out after he was benched in the second game of the season, as Ancelotti opted to play Alcantara instead.