Milinkovic-Savic has emerged as a target for Jose Mourinho as he looks to add to his midfield options at Old Trafford.
Although any deal will have to wait until after the World Cup, where the Lazio ace is currently on duty with Serbia.
Matic is playing alongside Milinkovic-Savic in Russia, with the duo starters in Mladen Krstajic’s midfield.
The latest reports indicate Matic is trying to get an answer out of his compatriot regarding where his future lies beyond the summer.
According to the Manchester Evening News, Matic has looked to find out how keen on a move Milinkovic-Savic is.
However, it seems Milinkovic-Savic is playing his cards close to his chest by refusing to speak at length about the matter.
That means Manchester United are not currently aware of whether the 23-year-old, who is under contract until 2022, is eager to call time on his Lazio stay.
United are said to have reservations about paying Milinkovic-Savic’s £88m (€100m) price tag due to his lack of Champions League experience.
But he remains in their sights, as well as those of fellow European heavyweights Real Madrid and Juventus.
Earlier this month, Milinkovic-Savic’s father revealed he has told his son to join Juventus.
“I’ve told him many times that Juventus would be perfect for him, the ideal club,” said Nikola Milinkovic.
“In Turin there is a prestigious club with multiple trophies that has been dominating the scene for years. He’d have the opportunity to grow and improve until reaching full maturity.
“After three seasons in Rome, Sergej knows the Italian championship perfectly, he has settled and integrated in a big way, he has learned the language well.
“With top quality teammates like Paulo Dybala, Douglas Costa and so forth, he could win the Scudetto, Coppa Italia and why not give an important contribution to triumph in the Champions League?
“Juve always go far in that competition and if they were to win the most prestigious trophy, Sergej could even dream of the Ballon d’Or.”
United, meanwhile, confirmed the signing of Fred as Michael Carrick’s replacement earlier this week.