The 22-year-old was allegedly the subject of a £25m bid from Liverpool in the summer, but Fluminense rejected the offer as they refused to part ways with one of their star players ahead of their run to the Copa Libertadores final.
Andre played in all 13 matches of the 2023 Copa Libertadores, including the final in which Fluminense beat Boca Juniors 2-1 after extra time to become South American champions for the first time in their history.
The four-cap Brazil international, primarily a defensive midfielder, has established himself as a first-team regular with Fluminense since making his senior debut in September 2020, making 169 appearances across all competitions.
Andre is expected to play for the 170th time in the famous garnet red, green and white stripes of Fluminense when they face Manchester City in the FIFA Club World Cup final on Friday.
The Citizens are not believed to be one of the English clubs interested in Andre, but Liverpool, Manchester United, Arsenal and Tottenham Hotspur have all been linked with the midfielder ahead of the New Year.
However, it is understood that Fulham are currently leading the race for Andre's signature, with the Evening Standard claiming that chief executive Alistair Mackintosh flew to Brazil for face-to-face talks last month.
Andre revealed in November that he would be open to a January exit from Fluminense after helping the club win the Copa Libertadores, and he has since revealed that it would be a "big dream" to play in the Premier League.
Speaking to Premier League Brasil, Andre said: "I watch the Premier League and it's a big dream to play there one day.
"I'm focused on finishing the season at Fluminense and realising my dream of winning the Club World Cup. But my dream is clear, to be a Premier League player."
It is understood that talks between Andre's representatives and Fulham are at an advanced stage and there is optimism from both sides that a deal can be agreed.
Fluminense are understood to value Andre, who still has just over two years remaining on his contract, at around £30m.
Fulham's pursuit of Andre comes at a time when the future of Joao Palhinha remains uncertain after the Portuguese midfielder missed out on a summer move to Bayern Munich at the 11th hour.
The Evening Standard also reports that the Cottagers are keen to sign Wolfsburg striker Jonas Wind as Marco Silva looks to provide competition for Raul Jimenez.