"Our aim is to do everything to hold on to Franck," Bayern general manager Uli Hoeness told Friday's edition of Bild. "But it's going to be a brutal fight - some clubs are going to table offers."
Reports in England this week suggested Premier League side City were planning to swoop for Ribery and his fellow Frenchman, Barcelona striker Thierry Henry, at the end of the season.
City, who failed in their audacious bid to buy AC Milan's Kaka in January, are determined to mount a sustained challenge on the English Premier League next season and have identified the French international as one of their key targets.
Other clubs likely to be interested in Ribery's services are Barcelona, Real Madrid and possibly Chelsea. But Bayern warned Friday that they were not about to let their prize jewel go without a struggle.
"The most important thing is to show that we know what we want and that we indicate that we want to keep him because if there's the slightest doubt his agents will try their luck," Hoeness said.
He added, "Franck and his family feel very comfortable with us here, but it's obvious that his agents are potentially interested in a transfer."
He went on to identify one factor that could trigger Ribery's exit from Jürgen Klinsmann's side, namely a lack of what he termed "prospects" in the quest for a European title.
"But I don't see any case of that at Bayern," ahead of Bayern's Champions League quarter-final clash with Barcelona.
With money seemingly no object for City's new Middle Eastern owners Hoeness concluded the interview by suggesting there was no sum which might tempt Bayern enough to contemplate losing one of their best players.
Ribery joined the Bundesliga giants from Marseille in July 2007 for 26 million euros. He quickly found his feet to become the talismanic leader of Bayern's midfield.
At the start of the year, Ribery hinted he would be prepared to leave Bayern, but the 25-year-old later issued a reversal insisting he will fulfill his contract, which expires in June 2011.
Bayern chairman Karl-Heinz Rummenigge spelled out this month precisely what Ribery meant to the side. "He is a crowd favourite, one of those players the supporters love, because he represents spectacular football and is synonymous with success."