Gazzetta says the midfielder, 26, could finally be set for a big-money move away from Italy's capital.
Milinkovic-Savic has long been linked with United as a potential partner for Paul Pogba.
With his deal not expiring until 2024, there remains no pressure for Lazio to sell.
But Milinkovic-Savic has already clocked up 240 appearances for the Serie A side in six seasons, with just one Coppa Italia to show for it.
Milinkovic-Savic is desperate to play regular Champions League football too.