The veteran forward comes off contract in June.
But Galliani says: "There is an agreement between me and Inzaghi: if we play in the Champions League he remains. Inzaghi will stay with us."
The Milan chief also confirmed plans to wind back transfer spending this summer.
"Silvio Berlusconi continues to be very fond of Milan," said Galliani, "but you cannot spend 810 million euros in five years like Inter ..."