The Dutchman has been linked with a summer switch to Old Trafford where he would reunite with former coach and fellow Dutchman Louis van Gaal.
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"Manchester United? That's not an option. I am staying at Bayern Munich. Period," he told De Telegraaf.
"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.
"Van Gaal and [Pep] Guardiola are the best coaches I have ever worked with. I am feeling well and I'm going nowhere. There's a zero per cent chance that I will join Manchester United.
"I think United did great to appoint Van Gaal."
Robben becomes the second Bayern player in as many days to rule out a move to Old Trafford following Toni Kroos's similar statement on Friday.