Vrsaljko has made 30 appearances for Atletico this season, including a brief cameo in the Europa League against Arsenal where he was sent off early in the game.
The Croatian is most comfortable as a right back but can cover across the defence, and at the age of 26 he certainly has his best years ahead of him.
However, with Atleti asking for more than €30million it could be the price that will put United off.
Mourinho is also rumoured to be interested in Fred from Shakhtar Donetsk and Alex Sandro at Juventus.