The Red Devils made no secret of their desire to bring in centre-half reinforcements during the summer transfer window of 2018.
Several targets were mooted, with Tottenham’s Toby Alderweireld and Leicester’s Harry Maguire considered to figure prominently on the Old Trafford wish list.
No deal was done, as United failed to make any additions in an area which had been prioritised, but interest remained.
Mourinho took in a trip to watch Serbia in action during the October international break, with Milenkovic believed to be among those he was keen to cast another eye over.
Fiorentina, though, have no intention of parting with the 21-year-old, or any of their other prized assets.
Chief executive Pantaleo Corvino told Gazzetta dello Sport of those to have attracted formal offers: “We rejected great offers from Lyon for [Jordan] Veretout, from Marseille for [Giovani] Simeone and from Manchester United for Nikola Milenkovic.
“[Aurelio] De Laurentiis pressed for [Federico] Chiesa. This is the right way to grow.”
It was suggested that United had rekindled their interest heading towards the January window.
Mourinho was, however, relieved of his managerial duties in December.
Ole Gunnar Solskjaer is now at the helm and bringing the best out of those already at his disposal.
He has hinted that there will be little movement before the latest deadline passes, with the Norwegian happy to work with his current crop.
“I'm happy with squad I've got,” Solskjaer said when quizzed on possible winter additions.
“I don't expect anyone to come in but obviously if the club have targeted and identified a few and I think they might fit here, I'll give my thumbs up. But it's not just my decision.
“Nobody had to tell me I had loads of talented players [to inherit at United]. I can see that from outside.”