The German giants could have cashed in on the France international in 2008, with Chelsea making an official bid and an enquiry from Real MadridBayern Munich turned down a big-money offer from Chelsea for Franck Ribery in 2008.
The France international was heavily linked with a move to Real Madrid at the time, but Rummenigge has made it clear that the Spanish giants were not the only team after Ribery's signature.
"Ribery is a hero with the fans and it's a good thing that we didn't give in when Real Madrid and a few more teams showed an interest in signing him in 2008," the Bayern chairman was quoted as saying by TZ.
"We solved everything like gentlemen with Madrid, although I must stress that there was no official offer. They made an enquiry and we closed the door on a move right away.
"We could have made a lot of money, because we also had an official offer from Chelsea that was utter madness. It was the right thing not to sell him, though.
"That showed all clubs that Bayern are a buying club rather than a selling club. That's the way it works with the big teams. You don't stand a chance if a team like Barcelona or Madrid don't want to sell and the same thing goes for Bayern these days."
Ribery, 30, signed a new contract with Bayern until the summer of 2017 last year and has stated more than once that he intends to retire at the Bundesliga champions.