According to Simon Jones of MailOnline, the Red Devils have been impressed by the 26-year-old this season and are ready to make a move for the Croatia international during the transfer window.
"While he is not the most physical of defenders, [Vrsaljko] can cover at left-back and has provided a number of attacking opportunities from his pinpoint crossing," Jones noted. "Jose Mourinho wants competition at right-back as Antonia Valencia has to manage wear and tear on his knees while the club have offers from Italy for Matteo Darmian."
Atletico would reportedly demand a fee of around £30 million for the full-back.
The Croatia international joined Atletico from Sassuolo for £14.5 million in the summer of 2016. It didn't appear as if the move was going to work out after he made just 11 starts in La Liga during his first season in Madrid, struggling to oust club stalwart Juanfran. However, he's been a more regular fixture under Diego Simeone this term, starting 19 league games, as well as Wednesday's UEFA Europa League final.
As Spanish football journalist David Cartlidge noted, the full-back was able to find some form in the new year amid doubts about his future at the Wanda Metropolitano:
Dermot Corrigan of ESPN FC praised the influence Vrsaljko can have when raiding down the right flank in January:
Vrsaljko's best assets are attacking ones, and he's given Atletico another outlet going forward in what is so often a defensive setup. His energy and delivery have finally made him a first-team regular.
In a Simeone side, defensive acumen is also vital, and while there is still work to do on that side of Vrsaljko's game, he has made strides in this regard during his time in the Spanish capital. Liam Twomey of ESPN FC felt the defender showed some signs of naivety in the recent Europa League semi-final clash with Arsenal:
United would be wise to reinvigorate this area of the squad. Valencia has become a tremendous right-back, but at 32, he's reaching the twilight of his career.
Atletico would surely be loath to sell the Croatia star. Having been patient with his development, Simeone is finally seeing the player flourish and will be confident of further improvement next term.
Additionally, with Juanfran coming towards the end of his career, it would be a blow to Atletico to lose a top-class successor. They will surely do what they can to withstand any approach from the Red Devils, who have the financial muscle to give the Madrid outfit a big decision to make.