Manchester United already have a replacement for Paul Pogba lined up.
The Independent says United's stance has altered with their position on Pogba being unsellable "already loosening".
Milinkovic-Savic has forged a reputation as one of Serie A's top midfield talents over the past couple of years.
And it would take a sizeable portion of the fee United would secure for Pogba in order to prise him away from Lazio.
The Italian press claim Mourinho's agent, Jorge Mendes, is close to Milinkovic-Savic and he could broker a deal for United.