Despite performing somewhat poorly thus far this season , Milinkovic-Savic featured as a substitute against Montenegro in the UEFA Nations League clash, with Serbia running out 2-0 winners.
A brace from Aleksandar Mitrovic, himself in fine form for Fulham, handed Serbia a historic win, in a game that marked the first time the two nations, who competed as one in the 2006 World Cup, have met competitively.
Alongside Milinkovic-Savic, Mourinho is also a reported admirer of Fiorentina defender Nikola Milenkovic, as he seeks to bolster his backline.
The 21-year-old, a centre-back who has scored twice already this season, played 90 minutes as Serbia kept a clean sheet, and Mourinho may well be tempted into the market.
It has been widely reported that the Portuguese was disappointed with the manner in which United's transfer business was conducted over the summer as they failed to acquire a new centre-back.
United have undergone a difficult start to the season after an indecisive window, losing three of their opening eight games, taking a total of 13 points, meaning they currently trail Manchester City, Liverpool and Chelsea by seven points.
Many ex-United players have had their say on this season's woes, with Zlatan Ibrahimovic, a trusted Mourinho lieutenant, insisting that the former Chelsea and Real Madrid manager is not the problem at Old Trafford.
“I think he has the ability to win [the Premier League]," he said. "I think he is the right coach for that club, for that team.
“But a coach is only as good as his team, so it’s not like he can do miracles if the team is not good enough.