Reports in the Spanish press over the weekend suggested that the Spanish club had made a €20million offer for the 28-year-old.
Galliani has moved quickly to deny those reports though, saying Montolivo is an "un-transferable player".
He also revealed that Montolivo is set to beat goalkeeper Christian Abbiati to the Milan captaincy following the departure of veteran Massimo Ambrosini.
"Sevilla's interest? We are talking about Milan's future captain, so an un-transferable player that won't be sold", Galliani said.
"I've spoken with [Christian] Abbiati, for him there aren't problems should the captain's armband be assigned to Montolivo. So we have assigned it to Riccardo."