The winger is keen to play alongside the former Dortmund star and thinks Franck Ribery deserves to win UEFA's Best Player in Europe award.
The Germany international, 21, recently made his Bayern debut after a lengthy spell on the sidelines due to injury and Robben is looking forward to teaming up with the former BVB star.
"Gotze's arrival? You have to believe in yourself and don't fear competition for places. I am really looking forward to playing alongside Mario," Robben told Bild. "He is a great player. One of our biggest strengths last year was that the absence of a key player didn't really weaken us.
"And it can be a positive thing as well when you occasionally miss a game in a season followed by a World Cup."
The Dutchman then went on to discuss Franck Ribery's nomination for UEFA's Best Player in Europe award and stated that his teammate is more deserving of the award than Lionel Messi or Cristiano Ronaldo.
"I would totally understand it if Ribery wins it. He deserves it. It would also be recognition for the team. It's the team that allows individuals to shine.
"Messi and Ronaldo are extraordinary, but Franck and Bayern won the treble."