Rummenigge insists they do not fear losing their best players to the Spanish side.
Real Madrid are reportedly still interested in Bastian Schweinsteiger and Philipp Lahm.
“Real Madrid have a great name, but Bayern are better and, at the moment, we are the more successful club,” the Bayern chairman told Bild.
“I think we can come to an agreement to extend the two deals until 2015.”
Rummenigge is keen for coach Louis van Gaal to sign a contract extension with the club.
He said: “We are very satisfied with Louis van Gaal’s work. We aim to extend his contract. I expect that we’ll know by Christmas what is happening.”
