Muller has made a fine start to 2015-16, scoring eight goals in as many games in all competitions after being linked with a big-money move to Old Trafford for much of the close-season.
Rummenigge, though, does not want Muller to ever leave the Allianz Arena and compared his situation to that of Messi and Rooney with their respective clubs.
“Muller will stay at Bayern, regardless of what any club offers,” the 59-year-old told Bild. “There is no amount that would make us consider an offer.
“Messi belongs to Barcelona, Rooney belongs to Manchester United and Muller belongs to Bayern. It should stay like that.