Serbia international Milinkovic-Savic is among Europe's most sought-after talents, and has been regularly linked with Manchester United and Juventus as well as Milan.
The 23-year-old midfielder would be welcomed at San Siro with open arms but, after bringing in Gonzalo Higuain and Mattia Caldara from Juventus in exchange for Leonardo Bonucci, Milan's technical director has talked down the prospect of another dramatic move late in the transfer window.
"In light of Financial Fair Play we won't be signing a top midfielder," Leonardo said at news conference to present Paolo Maldini as sporting strategy and development director.
"If we can find a way - within the rules - to pull off a miracle and sign a player who will bring a lot to the team then we'll try to do it. But we may not be able to.
"The deal we already did gives us a lot and stays within the rules, but it's very difficult to do again.
"Milinkovic-Savic is a dream for many teams, unfortunately right now dreaming about a player who is worth so much is not possible for us.
"Even a year ago when I was asked to choose one Serie A player [Milan wanted] he was the one I picked. He's the complete modern midfielder, but it's not financially possible for us to sign him."
Leonardo also dismissed rumours of interest in Paris Saint-Germain's Adrien Rabiot.