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"We are very proud to have one of the three best players in the world under contract; it is causing a bit of a stir in the transfer market but we have no intention of selling," Rummenigge told German tabloid Bild on Tuesday.
The 26-year-old Ribery, who is contracted to 2011 at the Bavarian giants, is also thought to be a Real target but Bayern's 60 million-euro price tag is reportedly causing the Spanish side to have second thoughts.
Reports from Madrid on Tuesday said that Ribery could be a Real player by the end of the week.
However the club's sporting director Jorge Valdano lamented the "astronomical sum" Bayern had attached to the French international.
"They don't want to sell and that is why they are proposing an astronomic sum."
According to Rummenigge, three clubs have already tabled concrete offers for Ribery - Chelsea, Manchester United and Barcelona - although he would not say for how much.