Chelsea made 'mad' Ribery bid, reveals Rummenigge
The French winger was an integral part of the Bayern squad that won five trophies in 2013 and was one of three nominees for this year's Ballon d'Or, losing out to Cristiano Ronaldo.
And Rummenigge admits his relief at having rebuffed interest in the 30-year-old from various clubs, including Real Madrid, in the past.
"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," he is 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."