The France international has already stated more than once that he wants to end his career at his current club and is set sign a new deal shortly
The 30-year-old's current deal with the Bavarians runs until the summer of 2015, but club CEO Karl-Heinz Rummenigge has revealed that the winger is close to inking a two-year extension.
"I can reveal that we have agreed terms in principle," Rummenigge told Bild.
"When Franck joined us in 2007, he had the reputation of being a player who switches clubs every one to two seasons.
"However, he has now already been here for six years. His family and he are feeling very good here in Munich."
Ribery joined Bayern from Olympique de Marseille in the summer of 2007 and has since made over 150 Bundesliga appearances for the Allianz Arena side.