Andre was linked with a move over the summer, as Liverpool conducted a midfield rebuild following the departures of Jordan Henderson, Fabinho, Naby Keita, Alex Oxlade-Chamberlain and Leighton Clarkson.
While the Reds recruited Wataru Endo, Dominik Szoboszlai, Ryan Gravenberch and Alexis Mac Allister, a move for Andre ultimately failed to materialise.
Despite failing to land Andre before the summer transfer window shut, Fluminense president Mario Bittencourt indicated that he would be open to discussing a winter transfer.
According to The Mirror, Liverpool have made the Brazil international one of their top targets for the January transfer window.
Fluminense were reluctant to allow Andre to depart before the end of the Copa Libertadores campaign, but South America's equivalent of the Champions League is now drawing to a close.
Andre has started all but one of Fluminense's 12 Copa Libertadores fixtures, including Wednesday's semi-final second leg against Internacional.
After drawing 2-2 in the first leg, Fluminense came from a goal down to win the midweek contest 2-1 and book their place in the final, which will take place at their home ground, the Maracana.
If Andre can help his side win their first-ever Copa Libertadores trophy in November's final against Boca Juniors, it would represent the perfect parting gift ahead of a potential January departure.
Andre, who rose through the youth ranks at the Brazilian club, has over three years left on his current deal which runs until December 2026.
The midfielder has previously admitted that he was "happy" to be linked with a move to Jurgen Klopp's side, but made it clear he was focused on his current club.
During his time in senior football, he has made 154 competitive appearances for Fluminense, chipping in with four goals and three assists.
After impressing for his club side, Andre earned his first international cap in June when he appeared as a substitute in Brazil's friendly defeat to Senegal.