Speculation linking the midfielder with a move to Stamford Bridge has been rife since Carlo Ancelotti left his position at Milan to take over the managerial reins at Chelsea. However, following reports last week that talks were underway, Galliani insists he has had no contact.
"We have not received any offers for Pirlo, not from Chelsea or any other club," he said.
Not denying that there is a strong chance of Pirlo making his San Siro exit this summer, Galliani did follow up his statement by strongly denying that Milan were monitoring Real Madrid midfielder Fernando Gago as a possible replacement for the 30-year-old.
"Pirlo is a Milan player," he said. "Hence, Gago cannot be our aim. If Pirlo leaves then we will see."
Chelsea have also been linked with Pirlo's teammate, 19-year-old Pato, for whom Galliani revealed Milan has received, and rejected, a "monumental offer".
Only last week the striker made a "come and get me" plea to Ancelotti, who signed him for Milan in 2007 from Internacional, but it would appear Milan are not prepared to surrender Pato's services for any amount of money.
"Milan this year has resisted a monumental offer for Pato," Galliani said. "But I will not say which club made the offer."