Erik ten Hag's side are believed to be on the hunt for a new centre-back amid uncertainty over the long-term future of Raphael Varane.
The 30-year-old Frenchman has entered the final six months of his contract at Old Trafford and he is free to negotiate pre-contract agreements with foreign clubs.
Jonny Evans is also out of contract this summer, but Harry Maguire still has 18 months remaining on his deal, while Ten Hag confirmed earlier this month that the Red Devils have triggered a 12-month extension clause in Victor Lindelof's contract.
Man United are thought to be in the market for a young central defender considering Lindelof will soon join Varane, Evans and Maguire in the 30+ age bracket, while 26-year-old Lisandro Martinez is the club's youngest first-team centre-back at present.
According to FootballTransfers, Man United have their sights set on 24-year-old Torino star Buongiorno, who could be available for €30m (£25m).
The report adds that members of Sir Jim Ratcliffe's INEOS group, who are the majority shareholders of French club Nice and recently purchased a 25% stake at Man United, believe Buongiorno would be a suitable addition to either club.
Buongiorno, who has also attracted interest from AC Milan, has developed into a first-team regular for Torino in recent seasons having previously honed his craft during loan spells at Capri and Trapani.
The 6ft 4in left-footed centre-back, who can also play at left-back, has made a total of 85 senior appearances for Torino in all competitions, including 16 Serie A starts so far this season.
Following an impressive string of performances for Torino at the backend of last season, Buongiorno was rewarded with his first international cap for Italy in June last year, before making his second appearance five months later.
Buongiorno is under contract at Torino until the summer of 2028 and is not the only centre-back on Man United's radar, as they have also been credited with an interest in Barcelona's Ronald Araujo.
A recent report claims that the Red Devils have made an enquiry for the Uruguay international, who is regarded as a leading transfer target for Ten Hag's side.
The likes of Bayern Munich's Matthijs de Ligt, Nice's Jean-Clair Todibo and Atalanta BC's Giorgio Scalvini have also been linked with a possible move to Old Trafford.