The Red Devils are allegedly preparing to move for a new centre-forward during the winter transfer window, with Rasmus Hojlund needing support in the final third of the field.
Hojlund has scored three times since his arrival from Atalanta BC, but he is yet to register in the Premier League, while Anthony Martial has also struggled this term, only managing one goal.
According to The Mirror, Barbosa has emerged as a genuine target for Erik ten Hag's side, with the Brazilian set to be available for around £20m in January, as his contract with Flamengo is due to expire in December 2024.
The report claims that Antony, who has struggled this season, could make the move to the Brazilian side on loan as part of the agreement.
Antony, 23, has not provided a single goal or assist in 10 appearances for Man United in 2023-24, and he again struggled to make his mark as a starter against Fulham on Saturday.
Red Devils head coach Ten Hag recently admitted that the "noise" surrounding the Brazil international has impacted his form in the opening months of the campaign.
Antony was recently given a leave of absence by Man United to deal with allegations of abuse which have been levelled towards him by his ex-girlfriend and at least one other woman.
The forward has been questioned by police in both Manchester and Sao Paulo, but he has always maintained his innocence and is said to be fully co-operating with police.
A short-term move away from Man United could therefore be beneficial, with Barbosa potentially moving in the opposite direction to boost the team's attack.
The 27-year-old started his professional career at Santos before making the move to Inter Milan in 2016, but he only managed one goal in 10 appearances for the Italian outfit.
Barbosa has rebuilt his reputation back in Brazil, boasting a record of 139 goals and 38 assists in 246 appearances for Flamengo in all competitions.
The forward has scored 18 goals and registered four assists in 53 appearances this term, although he has only netted five times in 23 league outings for the Rio de Janeiro outfit during the current season.
Casemiro, who is out for the next few weeks due to a hamstring issue, is Man United's leading goalscorer this season with four goals, while Marcus Rashford has only netted once.