The Rossoneri got off to a slow start to the campaign but have improved since the turn of the year to move up to third in the Serie A table.
Speculation had been mounting over Allegri's future with the club, but Galliani has insisted that he has not thought about any potential replacements.
"I'm in daily contact with Allegri, he will stay with us and I have not been in touch with any other coach," Galliani told La 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."
Allegri was appointed AC Milan coach in 2010.