The Daily Mirror is reporting that the Red Devils are interested in a potential deal to sign the 23-year-old playmaker in the 2018 summer transfer window.
The same article states that Milinkovic-Savic has been fundamental in Lazio’s challenge for a top-four finish under Simone Inzaghi in the current campaign.
The 23-year-old attacking midfielder has netted nine times and has made three assists in 26 appearances in Serie A this season.
According to the same story, La Liga giants Real Madrid and Ligue 1 leaders Paris Saint-Germain are both monitoring the former Genk star.
Manchester United are in second place in the Premier League table and 16 points adrift of leaders Manchester City in the one-sided title race.
The Red Devils lost 2-1 to La Liga side Sevilla in the Champions League round of 16 earlier this month.
The 20-time English champions will take on Tottenham Hotspur in the FA Cup semi-final at Wembley in April.
Manchester United signed Chile international Alexis Sanchez in a swap deal in the January transfer window.
The Red Devils won the Europa League and the League Cup last term.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news