The 23-year-old came through the youth system at Serbian side Cukaricki before going on to represent their first team on 86 occasions in all competitions.
Petrovic was signed by New England Revolution in April 2022, and he has since made 23 appearances for the MLS outfit, keeping seven clean sheets in the process.
According to journalist Tom Bogert, Man United are huge admirers of the goalkeeper and have been 'heavily scouting' him since his arrival in North America.
Bogert claims that there has not yet been any official contact, but the 20-time English champions are admirers of a player who has been capped on two occasions by the Serbian national team.
Petrovic, who last featured for Serbia against the USA in a friendly at the end of January, has a contract with his current side until June 2025, with the option of a further 12 months.
There is currently widespread uncertainty when it comes to the goalkeeping department at Old Trafford, with a turnaround potentially taking place during the summer.
Current number one David de Gea only has a deal at Old Trafford until the end of June, and it is understood that the club have not yet made a decision when it comes to the Spaniard.
However, a recent report claimed that Man United would be prepared to hand the 32-year-old a new deal providing that he takes a huge cut on his current £375,000-a-week pay packet.
Even if De Gea stays, there might be the need for at least one new goalkeeper this summer, potentially two, as Tom Heaton's deal is due to expire at the end of June.
Jack Butland is currently the number three stopper at the club, but the 29-year-old is only on loan from Crystal Palace, and as it stands, he will return to his parent side this summer.
Dean Henderson is spending the season on loan at Nottingham Forest, although it is believed that the England international will leave on a permanent basis this summer.
Leeds United's Illan Meslier has recently been linked with a switch to Old Trafford, while Atletico Madrid's Jan Oblak is believed to have admired by senior figures at Man United.
However, the Red Devils are unlikely to make any firm decision on their summer plans when it comes to a new goalkeeper until De Gea's future at the club has been decided.
Erik ten Hag's side are currently preparing to take on Barcelona in the second leg of their Europa League knockout round playoff, with the tie delicately poised following a 2-2 draw last week.