Earlier this week it was said that United are considering a January approach for Milenkovic, a towering Serbian centre-back, with the club have been linked with him for some time already.
Manager Jose Mourinho personally watched the 21-year-old in action for Serbia during the October international break and a Daily Mail report now claims the club will have eyes on Milenkovic when Fiorentina play Bologna on Sunday.
It is noted that Milenkovic, who has played as a right-back for Fiorentina this season despite typically being a central defender, is already a friend of United midfielder Nemanja Matic.
His current weekly wages are thought to be in the region of just £12,000, giving United massive scope to offer him an improved deal, although the Mail states that Fiorentina are likely to demand £50m, which would make him the most expensive defender in Old Trafford history.
While speculation regarding rumoured summer targets Harry Maguire and Toby Alderweireld seems to have dried up, it has already been suggested that United have another Serie A defender in mind as an alternative to Milenkovic should the Serbian prove unattainable.
That is Sampdoria and Denmark Under-21 international Joachim Andersen, a player who has also been linked with Juventus and Inter after making the switch to Italy in 2017.
As things stand, both Chris Smalling and Phil Jones are due to be out of contract at the end of the season, while Marcos Rojo has been linked with possible move to Wolves.