Pep Guardiola's side won the treble last year and have already wrapped up their defence of the Bundesliga ahead of their Champions League quarter-final against the struggling Red Devils.
Robben has 18 goals and 10 assists to his name this season and says that he and his team-mates are "razor-sharp" as they approach their European showdown.
"No team can have a stroll to the final," he told reporters. "We are facing Manchester United, a big name in world football, but we are razor-sharp. Our football is phenomenal and we want to show that more than anywhere in the Champions League.
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"We won the German league last week but we were not even bothered about that. Nobody in the dressing room was talking about it. We knew ages ago we would win the title."
Bayern won the Bundesliga earlier than any team in its history and Robben believes that their improvement even on last season's astonishing record is down to coach Pep Guardiola.
"Guardiola has turned us into the most dominant team in Europe," the 30-year-old remarked.
"We have made another giant step as a team this season. We are more dominant than we have been. From the very first minute we put massive pressure on our opponents and are capable of keeping the ball and putting them under pressure for the full 90 minutes.
"Our playing style is even more attacking than last year. This manager is tactically so strong. He is always pointing out where we can find the space to get one-on-one situations. He teaches us to make quick sprints and runs without the ball."