According to Simon Jones of the MailOnline on Thursday, the Red Devils have long been admirers of the 21-year-old, who has impressed for La Viola since arriving in Florence in 2017. The Serbia international has quickly cemented himself as an important player for Fiorentina.
"Fiorentina president Pantaleo Corvino values him at around £50 million, but he is on a relatively small wage of around £12,000-a-week," Jones wrote. "[He] is aware of United's interest and is a friend of international team-mate Nemanja Matic."
Jones reported there is also still interest in Harry Maguire of Leicester City and Napoli's Kalidou Koulibaly from United, although the Red Devils recognise signing such high-profile players in the midseason window may be a challenge.
Milenkovic could be more attainable, but Fabrizio Romano of the Guardian reported on Thursday that the Italian team rejected an offer of €45 million (£40 million) from Atletico Madrid for the Serbian in the summer. Romano added that Juventus also hold an interest in the defender.
Reports that Atletico and Juventus, arguably the two most defensively sound teams in European football, are eyeing Milenkovic is testament to how much progress he's made at Fiorentina.
Scouted Football noted that he'd been an ever-present for Fiorentina in Serie A in October, a trend that has continued throughout the course of the campaign:
Scouted Football @ScoutedFtbl
Youngest players to have played every minute for their clubs across Europe's top five leagues this season: 19y, 09m • 🇩🇪 Arne Maier 19y, 11m • 🇫🇷 Jules Koundé 20y, 10m • 🇨🇮 Ibrahim Sangaré 21y, 00m • 🇷🇸 Nikola Milenković 21y, 06m • 🇫🇷 Paul Bernardoni Young guns go for it. https://t.co/aUday9n47Y
Milenkovic has played at both right-back and centre-back this season, which are positions United have struggled in this term.
At 6'4", Milenkovic is unsurprisingly a colossus in aerial battles, and he uses his frame well to block shots too. The Fiorentina man is willing to put his body on the line, has sharp defensive instincts and is decent on the ball too.
Bleacher Report's Rob Blanchette a transfer would make sense for Jose Mourinho's side, noting they've had success signing a Serbian defender in January previously:
But Kaustubh Pandey of Calciomercato believes it'd be smarter for United to look elsewhere in their pursuit of a centre-back:
Kaustubh Pandey @Kaus_Pandey17
As much as I've liked what I've seen from Nikola #Milenkovic at #Fiorentina, #MUFC should look at a more established defender than the Serbian. He maybe a ball-playing version of Nemanja Vidic, but the situation United are in, they should look at more established options.
With Milenkovic tied to a contract until 2022, Fiorentina are under no pressure to sell. They also showed in the summer they are ready to dig their heels in against a big-money bid from a high-profile team.
But it would appear United are keen on Milenkovic. If he performs well until the January window opens, speculation about a move appears set to intensify.