The Rossoneri endured a disastrous start to the campaign but have rallied since the turn of the year and now sit in third place and are on track for Champions League qualification.
And though rumours have been rife regarding Allegri's future at San Siro, the club's vice-president insists he has not thought about identifying a potential replacement.
"I’m in daily contact with Allegri. He will stay with us and I have not been in touch with any other coach," said Galliani, in a video chat with Gazzetta dello Sport.
“Milan have had a very good season and I don’t see why we should change tactician. Allegri will certainly stay with us.
Galliani also gave his thoughts on the transfer market, saying that while the defence is the key area to strengthen, his preference is for Milan to produce players from within the club.
“Milan need to create top players, not buy them. If we make signings then we will sign a defender."