The Italian club's CEO has quashed speculation linking the midfielder with a move to Spain after appointing him as Massimo Ambrosini's replacement captain
Reports in Spain emerged over the weekend suggesting that Sevilla had tabled a £17 million offer for the midfielder, which was promptly rejected by the San Siro side.
Galliani has since moved to quash any further speculation over the 28-year-old's future, claiming he is in line to captain the side in the future after Massimo Ambrosini departed the club.
"We are talking about the future captain of Milan, the player [Montolivo] is not for sale," Galliani told Gazzetta dello Sport.
"I talked to [Christian] Abbiati before, he had no problem with Montolivo being named as the new captain.
"And then we assigned it to Riccardo, who among other things has a name that I always like to mention, since his footballing style reminds me of Kaka."
Montolivo established himself as a key player for Milan after joining the club from Fiorentina on a free transfer in the summer of 2012, scoring four goals in 39 appearances in all competitions for the club last season.