The 22-year-old was tipped to join the Reds as part of their midfield overhaul, which saw all of Fabinho, Jordan Henderson, Naby Keita, Alex Oxlade-Chamberlain and Leighton Clarkson depart.
Liverpool did make an approach to sign Andre over the summer, but their advances were rebuffed by Fluminense, who have the Brazilian under contract until December 2026.
Instead, the Reds brought in a quartet of new lynchpins in Wataru Endo, Dominik Szoboszlai, Ryan Gravenberch and Alexis Mac Allister, having also failed in their efforts to sign Jude Bellingham, Moises Caicedo and Romeo Lavia.
Szoboszlai and Mac Allister have already cemented regular starting spots for the Reds, who have taken 10 points from their opening four Premier League games during an impressive start to the season.
However, Fluminense chief Bittencourt has confirmed that his side would be open to doing business with Liverpool over the winter, and he confirmed that the Brazilian club turned down a summer approach from their Merseyside counterparts.
"Liverpool contacted me directly for Andre. I told their director: my friend, I don't sell Andre now," the Evening Standard quotes Bittencourt as saying.
"If you want to buy now to bring him in January, we can start talking. Or if you want to wait until December, we can do it."
While Liverpool have replenished their midfield ranks adequately this summer, the Reds do stand to lose Thiago Alcantara when his contract expires at the end of the 2023-24 season.
Thiago is believed to have turned his nose up to offers from Saudi Arabia to continue at Anfield, but the Reds will not stand in the injury-hit Spaniard's way of an exit next summer.
Nevertheless, the Reds also have Curtis Jones, Stefan Bajcetic and Harvey Elliott battling for minutes in the engine room, while Trent Alexander-Arnold has recently started taking up a midfield role for England.
A move for Andre is therefore unlikely to be a priority over the winter - especially with defensive concerns lingering - but the 22-year-old has put himself in the shop window thanks to his displays with Fluminense.
Primarily a number six, Andre has amassed four goals and three assists in 151 matches for Fluminense across all tournaments, including one strike from 43 games in the 2023 campaign.
The midfielder's solitary goal so far this season came in a Copa Libertadores quarter-final tie against Olimpia, as Fluminense advanced to the final four with a 5-1 aggregate win.
Andre also made his senior Brazil debut in a 4-2 friendly defeat to Senegal in June, and he has been called up to the Selecao squad for this month's 2026 World Cup qualifiers against Bolivia and Peru.