Muller had been tipped for a move to Old Trafford to link up with United boss Louis Van Gaal, under whom he made his Bayern debut in 2009.
The 24-year-old subsequently ended speculation about his future by signing a five-year contract extension with the Bundesliga giants.
But when asked whether he knew of United's interest, Muller told Germany's Sport Bild newspaper: "Of course - I was aware I could theoretically earn more with a transfer.
"The sums that were standing by from foreign clubs were already astronomical. I can only say that a change was never really an issue anyway."
Muller proved one of the stars of Germany's victorious World Cup campaign, scoring a hat-trick against Portugal and further goals against the United States and Brazil.