That’s the claim of the Guardian.
The Red Devils are willing to meet Jose Mourinho’s demands and bring in a new centre-back in the January window.
And Serbian international Milenkovic – who can also play at right-back – has emerged as an alternative target to the likes of Tottenham’s Toby Alderweireld and Inter Milan star Milan Skriniar.
Milenkovic has started in all 12 of Fiorentina’s Serie A games this season, scoring two goals, having joined from Bologna a little over 12 months ago.
And Mourinho has identified the 21-year-old as one player who could improve United’s leaky back-line.
They have conceded 21 goals in just 12 games in the Premier League and sit down in eighth, as many as seven points off of the top four.
The Guardian say that Milenkovic – who played in all of Serbia’s World Cup games – was the subject of €45m (£39.8m) bid from Atletico Madrid in the summer.
That could mean United are forced to pay in excess of £50m – more than they have ever paid for a centre-back before.
United will send scouts to watch the towering Serb when Fiorentina take on Bologna on Sunday (2pm).
He remains under contract until 2022 but is paid just £10,000-a-week by Fiorentina on the deal he signed in joining from Partizan Belgrade.
Sky Sports have claimed that another Serie A defender – Sampdoria’s Joachim Andersen – has been eyed as another target.
But Juventus are also interested in the 22-year-old, as are Inter Milan. It is claimed both clubs have even made early contact over a possible January deal.
Former United front-man Dimitar Berbatov has urged United’s board to sign whoever Mourinho identifies as his first-choice target.
Berbatov told the Daily Mirror: “They need to reinforce at the back especially centre backs, one or two.
“In every other position they have several quality players and everything they need, so just defence needs reinforcing. Hopefully they can find one or two and then they should be okay.
“It’ll be more difficult in the winter transfer window than the summer one to make signings for Mourinho but he should be able to find one person he wants to bring in.
“So if there is someone he wants to bring in the board should listen to him because it’s obvious that the club aren’t perfect right now and aren’t in the position that they want to be in.”