Robben has been linked with United ever since it was announced that Louis van Gaal would be taking over at Old Trafford after the World Cup.
Robben told Dutch broadcaster NOS following Holland's 3-0 win over Brazil that Van Gaal had offered him a place in the United squad next season.
The winger says he shares a "special bond" with Van Gaal, but that does not mean he will be following the new United boss to Old Trafford for the new season.
"I have a special bond with him. He is the most important coach in my career," Robben said.
"(Moving to United) is not an option though. I will stay at Bayern Munich."
Robben has been in top form under Van Gaal's stewardship at the World Cup.
The former Chelsea winger has made the short list for player of the tournament after scoring three goals and making one assist during Holland's run to the last four.
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- Louis van Gaal