Mueller was one of the stars of the World Cup in Brazil, scoring five goals and claiming three assists as Germany won the trophy, and the brilliant forward unsurprisingly attracted attention from rival clubs.
United were reportedly one of the interested parties, with new manager Louis van Gaal giving the then 19-year-old Mueller his debut at Bayern at the start of the 2009-10 season.
However, Mueller says he never had any intention of leaving Bayern.
When asked whether United offered him millions more to leave the Allianz Arena, he told Sport 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.”
In Reus's case, however, the news emerged not from the player himself, but from Atletico Madrid president Enrique Cerezo.
Cerezo, being quizzed by the Spanish press ahead of Tuesday's Super Copa match against Real Madrid, was asked about Reus - who had been hotly tipped to join the Spanish champions this summer.
But he denied any knowledge of a potential deal - and said that given United had failed to broker a sale, Atletico never had a chance:
"I don’t know where the Marco Reus rumour came from. It’s a player who, at this time, is impossible to us," he said.
"Look, he had an offer for a lot of money from Manchester United and he has not gone… we will not sign him with a lesser offer."
- Sports & Recreation
- Manchester United
- Marco Reus