The 22-year-old was heavily linked with a move away from his Brazilian club during the summer transfer window, with Liverpool thought to have made the strongest attempt to sign him.
Andre ultimately remained with Fluminense, though, and he helped his side win the Copa Libertadores earlier this month courtesy of a 2-1 win over Argentina giants Boca Juniors.
The Brazilian will also represent his team in the Club World Cup in December, but he is then set to leave next year, potentially during the January transfer window if a deal can be agreed.
Arsenal continue to be heavily linked with the midfielder, with the Gunners looking for a long-term partner for Declan Rice in the middle, while Liverpool are expected to reignite their interest in 2024.
However, according to FootballTransfers, Man United have now made an approach, with the Red Devils determined to secure his signature.
The report claims that a number of Premier League clubs have been in touch with Fluminense to register their interest, and it is possible that he will leave in January for European football.
Casemiro is currently being heavily linked with a move away from Man United, with teams from Saudi Arabia believed to be keen to sign the ex-Real Madrid midfielder.
Fluminense would reportedly want between £30m and £40m for Andre, who recently revealed that he was open to moving clubs at the turn of the year.
Fluminense president Mario Bittencourt recently admitted that he expects to receive a club-record bid for the South American after the Club World Cup.
"We are waiting. Today, there is no concrete proposal for Andre," Bittencourt told Ge. Globo. "But we are sure that after the World Cup - he will play in the World Cup - a stratospheric proposal will arrive.
"It could be the biggest sale in the club's history. We could possibly lose both (Andre and defender Nino), but we are working to replace them."
Andre has a contract with Fluminense until the end of 2026, and he has represented his current side on 162 occasions in all competitions, scoring four times and registering three assists.
Man United are expected to sign a new central midfielder next year even if Casemiro stays at the club, while the Red Devils are also believed to be planning to move for a centre-forward in January, with Porto's Mehdi Taremi thought to be their leading target.