According to Mundo Deportivo, Red Devils manager Jose Mourinho is eager to add two more midfielders to his squad over the summer (via MailOnline's Robert Cottingham). United are said to have sent scouts to cast their eye over Milinkovic-Savic in April.
The Serb has a number of other suitors, including Real Madrid, Paris Saint-Germain, Chelsea and Tottenham Hotspur, but United are reportedly leading the race as Barca balked at Lazio's hefty asking price.
Milinkovic-Savic, 23, has been a key part of the Lazio first team for the past three seasons and is enjoying a successful 2017-18 campaign.
In Serie A this term, he has netted 11 goals and provided three assists in 32 appearances from central midfield.
He is able to operate as a No. 10, particularly in a 4-2-3-1 formation, but his preferred position is in the middle of the park, perhaps in a 4-3-3 system, where he can contribute both in defence and attack.
Along with his fantastic technique, passing range, ball control and maturity, he is also a physically imposing player and threatening in the air, as WhoScored.com highlighted:
United are one of few clubs who boast the financial clout to meet Lazio's asking price, and Milinkovic-Savic has previously labelled Mourinho as "the best manager in the world," per Sky Sport Italia (via Football Italia).
United are not short on options in midfield. But Scott McTominay and Nemanja Matic are more defensive-minded players, Michael Carrick will be retiring at the end of the season and Marouane Fellaini could soon depart Old Trafford, as his contract expires in the summer.
The prospect of Milinkovic-Savic playing alongside Paul Pogba in United's midfield will be exciting for United fans, and it could become a reality if Barca have pulled out of the running for the Serbia international.