The German World Cup winner has been linked to Old Trafford in the past, but Stoiber has warned the Red Devils not to bother making an approach in the future.
United were successful in signing Bastian Schweinsteiger from Bayern in 2015, but after just one year at the club, the midfielder has dropped out of the first team.
When asked about a potential move to United for Muller, Stoiber told Bild: "It should not be happening that someone like Thomas Muller plays for Manchester United.
"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."
Since making his first-team debut in the 2008-09 season, Muller has won five Bundesliga titles, four DFB-Pokals and the Champions League trophy.