United had submitted an improved offer for the player last week, whose contract at Bayern runs to 2019.
Bayern Munich said they have no interest in selling Thomas Mueller, despite a reported offer from Manchester United to sign the versatile attacking midfielder.
"It is not Thomas who has caused this furore but his performances," Bayern sports director Matthias Sammer was quoted as telling Sport Bild magazine on Wednesday.
"For everything that has followed there is nothing we can do. (Bayern CEO Karl-Heinz) Rummenigge was right when he said that he is a player who does not have a price tag."
Sport Bild said United had submitted an improved offer for the player last week, whose contract at Bayern runs to 2019.
United have already signed Bayern's talismanic midfielder Bastian Schweinsteiger and the German champions are desperate to hold on to Mueller, designated to succeed Schweinsteiger as the team's leader.
A youth product of Bayern, the 25-year-old Mueller, who won the World Cup with Germany last year, clinched the Champions League with Bayern a year earlier and is chasing a record fourth straight Bundesliga title this season.
He was promoted as a regular starter to the first team under current United coach Louis van Gaal when he was at Bayern between 2009-2011.