Milan technical director Leonardo said "there was never a negotiation" for Milinkovic-Savic, via Football Italia.
"I talked to his agent, [Mateja] Kerman, but we've had a relationship for many years," Leonardo added. "There was never a negotiation, partly because we knew it was something that isn't feasible right now.
"He costs a lot and doesn't fit with our parameters. Our operations were all linked to exits and it wasn't easy."
Earlier Friday, Italian business newspaper Il Sole 24 Ore (h/t Chris Wright of ESPN FC) reported the Rossoneri had agreed a deal worth €40 million (£36 million) with Lazio that would see the Serbia international move to the San Siro on loan for a season with an option to buy.
The deadline for Serie A clubs to sign new players is 7 p.m. BST on Friday.
Calciomercato.com recently reported that Milan's offer to Lazio for Milinkovic-Savic is structured in such a way as to comply with financial fair play rules and could culminate in the Rossoneri shelling out a further €70 million (£63 million) to sign him permanently next summer.
Milinkovic-Savic enjoyed a breakout campaign in 2017-18, producing consistently good performances that led to his linking with some of Europe's biggest clubs.
He netted 12 goals and provided three assists in 35 Serie A appearances and showed a range of attributes boasted by only the most complete central midfielders.
The Serbia international would be a fantastic addition to Milan's engine room and join a squad that has already been bolstered this summer by Gonzalo Higuain's addition.
Milinkovic-Savic's signing would have topped off a brilliant summer transfer window for the Italian giants and give Milan fans hope of finally returning to Serie A's top four for the first time since 2013—and perhaps even competing for the Scudetto.