Muller has been linked with a move to Manchester United but Rummenigge does not expect the Germany international ever to want to leave the Bavarian club and has therefore offered him a position after he hangs up his boots.
“I get the feeling that Thomas will never leave FC Bayern,” Rummenigge told Sport Bild magazine.
“And when Thomas does call it a day, we would also like to keep him as part of the club.”
There had been fears that Muller might follow Bastian Schweinsteiger to United for a reported 100 million euro, but Rummenigge said last week that he is not entertaining that idea, adding that the 25-year-old is priceless.
Bayern have already signed midfield cover with Arturo Vidal arriving from Juventus on Wednesday.
The Chile international joined for 37 million euro from the Italian champions with a further three million euro owing based on the player reaching certain objectives in Bavaria.