Manchester United scouts checked on Sergej Milinkovic-Savic last week.
Jose Mourinho wants two new midfielders for the summer and the powerful Milinkovic-Savic has been impressing for Lazio this season.
However, he struggled to make an impression last Thursday, under the scrutiny of United staff, as Lazio lost 4-1 to Red Bull Salzburg in the Europa League.
The 23-year-old has scored 11 goals this season and is valued at £89million by his club.
United need to replace Michael Carrick and Marouane Fellaini.
They have also made an offer for Shakhtar Donetsk midfielder Fred. The Brazilian is wanted by Manchester City too though the newly-crowned Premier League champions are understood to have offered less than United for the £50m-rated 25-year-old.