United previously lured Schweinsteiger away from the Allianz Arena and have been linked with a move for Muller on more than one occasion.
Nevertheless, supervisory board member Edmund Stoiber has stressed Muller's situation is nothing like that of Schweinsteiger back in 2015.
"It should not be happening that someone like Thomas Muller plays for Manchester United," Stoiber told Bild.
"The fans were already a bit unhappy when Schweinsteiger left us for Manchester United. But he was already 32 and wanted a new challenge. But our fans and members would never forgive us if we sold Muller.
"He is the opposite of someone like Cristiano Ronaldo. He is much more than just a great player. Muller is part of our DNA.
"He represents key values for us and is someone the fans love."
Muller has made over 350 appearances in all competitions for Bayern since breaking into the first team in 2008-09, winning five Bundesliga titles, four DFB-Pokals and the Champions League over the past nine seasons.