A move failed to materialise this summer but newspaper reports in his native Serbia have claimed that could soon change.
The reports state Manchester United boss Jose Mourinho will be in attendance to watch the 23-year-old during Serbia's clash with Montenegro on Thursday night.
Milinkovic-Savic only recently extended his deal with the Rome club until 2023, but that hasn't stopped United planning a move for the January transfer window.
The Premier League giants will have competition as it is reported Real Madrid, AC Milan, Juventus and PSG are all interested in the former Genk man.
But according to Serbian football scout Goran Milosavljevic, who spent 15 years working for Arsenal in the Balkans, believes it would be an unwise move for Milinkovic-Savic.
In an exclusive interview with Tribalfootball, Milosavljevic advised the playmaker to spend more time honing his craft before moving to one of Europe's big clubs.
"I don't think so," Milosavljevic told Tribalfootball when asked if Milinkovic-Savic was ready to leave. "I think maybe in a few years. At the moment he is not ready, he doesn't have enough quality.
"He played at the World Cup and his price went down because of his performance. Physically and quick-thinking need work.
"He also needs to work when his team doesn't have the ball. Steven Gerrard played in the same position and he ran 14km for a game with many sprints."
In 131 appearances for Lazio, Milinkovic-Savic has scored 25 goals and provided 21 assists.