The 34-year-old duo are due to see their current deals expire in the summer and both have admitted to being unsure about their futures.
Recently-retired Netherlands international Robben scored in Bayern's 6-0 win over Hamburger SV at the weekend, while Ribery also rolled back the years by finding the net twice.
Asked whether the pair still have a part to play at the Allianz Arena, 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."
Robben will play no part in Wednesday night's Champions League last-16 second leg against Besiktas due to injury, with Bayern leading 5-0 ahead of the trip to Portugal.