The San Siro side's CEO has made it clear that the Spain international will not move to Italy as he expects the midfielder to stay with Arsene Wenger's men this summer
Fabregas is continually being linked with a move to the Camp Nou giants, while recent reports linked AC Milan with a move for the playmaker, but Galliani thinks the 24-year-old will stay at the Emirates.
"Fabregas costs an astronomical amount of money and is not one of our objectives at the moment. He will stay at Arsenal rather than move to Barcelona as far as I know," Galliani was quoted as saying by La Gazzetta dello Sport.
The supremo also discussed AC Milan's summer transfer targets, and ruled out a move for Bayern Munich's Bastian Schweinsteiger.
He said: "Schweinsteiger? No, he's a key player at Bayern and is not a transfer target for us. There has been enough talk of 'Mister X' [AC Milan's alleged transfer target]. If we make a big signing, it will happen late in August."
AC Milan have so far already secured the services of Taye Taiwo, Philippe Mexes and Stephan El Shaarawy and are widely expected to make a move for another midfielder later this summer.