The experienced Dutch winger has already confirmed that he will be bringing a 10-year spell with the German champions to a close in 2019.
Robben, who is prepared to consider retirement if no suitable offers arrive, will be moving on at the age of 35.
His fellow wideman Ribery will be a year older by the time the 2018-19 campaign comes to a close and is set to become a free agent after 12 years in Bavaria.
Bayern president Uli Hoeness admitted after a recent victory over Werder Bremen that two stalwarts were approaching the end, and sporting director Hasan Salihamidzic has reiterated that stance.
He said in Sport Bild of Ribery’s future: “The president talked about it [the possibility of leaving], and I think it will be like that. It's a year of changes.”
Salihamidzic admitted of a man who has made 406 appearances for Bayern: “I am pleased that Franck is still playing that well. He's one of our key players.”
Ribery has been able to shine this season after seeing fellow Frenchman Kingsley Coman suffer an untimely knock.
The 22-year-old has suggested that he will consider hanging up his boots if he is forced to undergo a third operation on a serious ankle injury.
He told Telefoot: “I don't think I'd have a third operation. Even if I protect myself and I try to be careful, if I get injured again it would be too much.
“Enough is enough. Perhaps my foot isn't up to it, and I'll go and get on with my life.”
Salihamidzic doubts that things will get that serious for Coman, with an exciting talent expected to return to action once though a period of rehabilitation that will test him mentally and physically.
“Rehab is no fun,” said the former Bayern star.
“I'll talk to him. I tore my ACL twice in one year and had similar thoughts.
“I think the world of Kingsley. He's got a great future.”