The Rossoneri CEO has quashed speculation linking the midfielder with a move to Spain after appointing him as Massimo Ambrosini's replacement as skipper
Reports in Spain emerged over the weekend suggesting that Sevilla had tabled a €20 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.
The Italy international donned the captain's armband for the first time in November last year, when he inspired Milan to a 1-0 win over eventual Serie A champions Juventus.