The appointment of Louis van Gaal as manager at Old Trafford has seen Robben linked with a summer switch to link up with his fellow Dutchman.
Robben has experience of the Premier League following a previous stint with Chelsea, but he has made it clear that he has no intention of returning to English football.
The 30-year-old signed a contract extension at Bayern in March to keep him at the club until 2017, and despite his admiration for Van Gaal he is not interested in a reunion.
Speaking to Dutch newspaper De Telegraaf, Robben said: "Manchester United? That's not an option. I am staying at Bayern Munich. Period.
"And I cannot imagine that Bayern would want to sell me.
"I have only just renewed my contract and we are happy with each other. It would have been a different story had I been unhappy.
"I would have been open to a move then, because I had a great time under Van Gaal at Bayern. He has been very important for my career. However, fact is that I am very happy at my current club."
Robben will play under Van Gaal for the Netherlands at the World Cup this summer before the manager takes up his post at Manchester United, and the former Chelsea man feels he was the perfect choice to replace David Moyes.
"I think United did great to appoint Van Gaal," said Robben.
Robben's announcement that he is committed to Bayern comes just a day after team-mate Toni Kroos revealed that he expects to stay with the Bundesliga champions.
Kroos has also been mentioned as a transfer target for United, but he does not expect to be on the move this summer.
"I am expecting to play for Bayern Munich next season," said Kroos in a statement to BILD.
"There was a lot of speculation, but Manchester is and was not an issue.
"At this point in time I am fully focused on preparations for the 2014 FIFA World Cup."