The veteran comes off contract at the end of June.
“I'd like to stay in Florence," Ribery told the official Bayern Munich YouTube channel.
“I like Florence a lot, the city, the people, the fans, the language – I like a lot of things. It was brilliant for two years, it was a great experience.
“I hope it will carry on for one or two years. My position is: I want to stay at Fiorentina. You know my mentality: I love to work. I have lots of fun on the pitch and enjoy it as well.
“I feel very good and I'm still fit. That's good."