"I can guarantee that they will stay," said Bayern CEO Karl-Heinz Rummenigge. "But not just these two. We will not sell any key players."
Bayern are fourth in the Bundesliga, a point behind Hanover 96 with five games left, and are desperate for a top three finish to compete in Europe's top club competition next season with the final to be held in Munich.
A fourth-place finish would mean playing in the Europa League.
Dutch winger Robben, who has a contract until 2013, has said competing in the Europa League would be worse than not playing in Europe at all.
The 27-year-old has played 52 Champions League games with four different teams since making his debut in 2002.
Frenchman Ribery last year extended his contract to 2015 with the Bavarians, who sacked coach Louis van Gaal on Sunday and replaced him with interim Andries Jonker.
Bayer Leverkusen's current coach Jupp Heynckes will be taking over at the end of the season.
Rummenigge also said Bayern would be active during the summer transfer window even if they missed out on the Champions League.
"Transfer decisions do not depend on that," he told Bild newspaper. "We played in the UEFA Cup in 2007 but we still brought Ribery, Luca Toni, Miroslav Klose and Hamit Altintop."
"We will decide on these things together with Jupp. But one thing is certain: We will buy players."
‘The fact he’s on a short deal doesn’t sit well. Gareth laid the foundations for players coming through. All Tuchel’s got to worry about is the here and now’: England hero lays out his issues with Thomas Tuchel appointment
‘England supporters are craving some success. If Tuchel can come in and finish the brilliant job Gareth Southgate started, nobody will care if he leaves’: Ex-Three Lions international gives his take on Thomas Tuchel's short-term deal
