Manchester United have been tipped to sign Milinkovic-Savic despite landing Fred from Shakhtar Donetsk last month.
The Lazio bulldozer, who impressed amid a poor World Cup campaign for Serbia, is in-demand with Europe’s elite all eyeing a transfer.
Manchester United appeared to have cooled their interest in Milinkovic-Savic.
But Italian newspaper Il Messaggero claim United have stepped up their bid to sign theplayer amid interest from Real Madrid.
The La Liga giants have money in the bank from Cristiano Ronaldo’s move to Juventus.
The 33-year-old moves to Turin in a £105million deal and that money, as well as his wages, could fund a Milinkovic-Savic transfer.
United, however, have also entered talks with Lazio over a deal.
But where he ends up remains to be seen.
The Red Devils have Paul Pogba, Marouane Fellaini, Ander Herrera, Fred and Nemanja Matic on their books.
Yet Pogba may leave for a new challenge elsewhere having clashed repeatedly with Jose Mourinho last term.
Fellaini signed a two-year deal but he, too, could leave in 12 months time if he fails to sparkle.
Meanwhile, Milinkovic-Savic hinted at a Lazio exit earlier this month.
“Every day I see a different team interested, it’s a stimulus,” said Milinkovic-Savic.
“Juventus is a great team, at the top in Italy. My brother also lives in Turin, the family is important to me.
“To the Lazio fans I would like to say that I’ve had three wonderful years, in any case, they will remain in my heart.
“Now I will head back to see if I will stay or leave. Italy or abroad? I’ll think about it in a few days.”