The Germany international was a target for new Red Devils boss Louis van Gaal, who worked with Muller during his time in charge of Bayern between 2009 to 2011.
Muller recently committed his long-term future to the Bavarian giants by signing a contract extension at the Allianz Arena until June 2019.
And the 24-year-old, who helped Pep Guardiola’s troops retain the Bundesliga and DFB-Pokal titles last season, insists a transfer was never on the cards for him.
He told Bild: “I can just say: a transfer for me was never an option. FC Bayern is my club.
“I knew that I would have earned more money,” added Muller on the bid from United. “The sums from other clubs which circulated had been astronomical.”
The Bayern youth product helped the German national team claim a fourth World Cup trophy last month, scoring five goals in the tournament as Joachim Low’s side went on to beat Argentina 1-0 in the final.