The German World Cup winner was linked with the former Premier League champions before he put pen to paper on a new contract with the Bundesliga giants this summer.
The 24-year-old told Bild: "I knew that I would have earned more money. The sums from other clubs which circulated had been astronomical. I can just say, a transfer for me was never an option. FC Bayern is my club."
United have been criticised for the lack of transfer activity at Old Trafford this summer, having only signed midfielder Ander Herrera and Luke Shaw in the early stages of the window.