The chief executive at the Allianz Arena has revealed that the door is open for both of them to remain with the Bundesliga leaders beyond the end of their current deals, which are due to expire this summer.
Both players are now 34 years of age but proved their worth in the 6-0 romp against Hamburg at the weekend with Ribery scoring twice while Robben also found the net.
The latter has also retired from international football with the Netherlands to try and extend his career and it seems that could be with Bayern.
Rummenigge told reporters: ‘We have spoken with both players and agreed to hold contract talks in April and then we’ll see.
‘It’s true, Franck has played superbly this Saturday, Arjen too. Both scored great goals. In April we’ll talk. This has been agreed with the players and both of them accepted that. It was very unproblematic for them.
‘We have the task to put together the squad for the next season and we will do that to our best knowledge and ability. That wasn’t a problem for either of the two.
‘It is known that generally, speaking for both of them, they would like to remain at Bayern Munich and, if they’re playing like they did on Saturday, we’ll get together and talk about it.’
Pivotal game in Group E almost a pick ‘em with the bookies