The Red Devils are said to be planning to move for a new centre-forward during the winter market to ease the pressure on Rasmus Hojlund.
The 20-year-old has shown plenty of promise during his early career at Old Trafford, finding the back of the net on three occasions in three Champions League appearances, but he is yet to net in eight Premier League outings.
Anthony Martial has only scored once this season and is out of contract next summer, meanwhile, with the Frenchman widely expected to move on.
Barbosa has been linked with a move to Man United, and a recent report claimed that the English giants were prepared to let Antony move in the opposite direction on loan.
However, Antony's agent has allegedly firmly rejected such suggestions, and the potential swap deal has now been rubbished by the Flamengo vice-president.
During an interview with O Globo, Braz was questioned on the reports and said that there was "zero chance" of such a deal occurring at the start of 2024.
Barbosa has scored 18 times and registered four assists in 53 appearances for Flamengo this season, but his contract with the club is due to expire at the end of December.
According to journalist Vene Casagrande, the forward is in talks with the Brazilian deal over a new deal, with both parties keen to continue their relationship.
The 27-year-old has scored 139 goals and registered 38 assists in 246 appearances for his current side in all competitions since making the move from Inter Milan in 2020.
Barbosa, who is an 18-time Brazil international, scored 56 goals in 154 appearances for Santos ahead of a move to Inter in 2016.
However, he failed to make his mark with the Italian giants, only managing one goal in 10 appearances.
Man United's attacking problems this season are demonstrated by the fact that Casemiro, who is currently on the sidelines with a hamstring issue, is their leading goalscorer with four goals.
Marcus Rashford has only netted once during a disappointing campaign to date, with Bruno Fernandes, Scott McTominay and Hojlund joint-second in the list on three.