The Dutch international's current deal at Allianz-Arena is due to expire at the end of the season and the club recently held talks over a contract extension, although no agreement has yet been reached.
Franck Ribery has already penned a new deal with the reigning Bundesliga champions and Rummenigge is confident Robben will soon follow suit.
"We have also spoken with Robben over a contract renewal," Rummenigge said at a fans' event. "He wants to wait until Christmas, but there is nothing to suggest we will not agree a one-year renewal with him as well. I think things will work out."
Rummenigge believes both Robben and Ribery still have a lot to offer the Bayern cause despite both players seemingly reaching the latter stages of their careers.
"Ribery and Robben might be turning 34 and 33, respectively, but they still give us something extra," Rummenigge added.