According to reports in the 'Daily Mail', 'La Viola' have told Manchester United that they will need to part with a sizeable sum for the 21-year-old.
However, it is believed that this goes way over the 'Red Devils' valuation of the player, although this could be part of Fiorentina's plan.
With Juventus also showing an interested, the club from Florence are hoping that this might spark a tug-of-war, taking the price higher.
Milenkovic has eight caps for Serbia, playing all three of their games at the World Cup this summer.