Muller had courted interest from the Premier League giants earlier in the transfer window and previously claimed to have turned down "astronomical" figures to join United.
"I know there was interest, but Man United were interested in a lot of players this summer," he told The Guardian.
"It never really got anywhere because I had just renewed my contract [until 2019], and Bayern were clear that they saw my future here. The decision for me was an easy one."
Muller, who helped Germany to World Cup glory in July, has scored once in three games for the Bavarians so far this season.