According to The Guardian, United executive vice-chairman Ed Woodward has promised to spend £100m-plus this January in order to replenish Jose Mourinho's squad.
Along with a back-up striker to relieve Romelu Lukaku, Mourinho desperately wants to add another centre-back to his ranks.
Milenkovic is another name that has surfaced in recent weeks after his strong start to the season with Fiorentina.
The 21-year-old was named by ESPN earlier this week as one of three Serie A centre-back targets that Mourinho has provided Woodward, along with Inter's Milan Skriniar and AC Milan's Alessio Romagnoli.
The Portuguese attended Serbia's Nations League clash with Montenegro earlier this month to personally assess Milenkovic.
Given his age and inexperience, there are concerns that Milenkovic would need an adjustment period at Old Trafford.
But Bertuzzi, a former talent scout for the Florence club, insists the 6ft 5in stopper possesses enough maturity and poise to cope with the rigours of England's top flight.
"I followed him for a long period, he has been targeted by [Pantaleo] Corvino a long time ago. I was amazed by his coolness and his strength," Bertuzzi told Tribal Football.
"Milenkovic is a mature man. He lacks in positioning, that's why [Stefano] Pioli plays him decentralised.
"I think it is probable to see him doing well in Premier League, because he improved a lot in just one year at Fiorentina."
After a slow start following his move from Partizan Belgrade in the summer of 2017, Milenkovic has emerged as a key member for Stefano Pioli's side.
He has started every Fiorentina game since the middle of April and also featured in all three of Serbia's group games at the 2018 World Cup.