Luiz has not played in the Premier League for Chelsea since October after being involved in a heated row with the Blues boss following defeat against Roma.
He was subsequently dropped for the game against Manchester United and has played just once, the 4-0 win over Qarabag last month.
Andreas Christensen was instead drafted in with Conte later explaining the Brazilian needs to work hard to regain his spot.
A knee injury has kept him out of action recently but it is thought the Italian coach favours Christensen over Luiz.
And the Sunday Mirror claim the Brazil international’s days at Stamford Bridge are numbered.
It is reported that Juventus lead the race for Luiz’s signature, who would be available for just £23million.
However, Manchester United could also make a surprise move for the 30-year-old with Jose Mourinho keen to bring in more defensive reinforcements next month.
Conte has previously offered no promises over Luiz’s future at the club, instead praising Christensen’s recent displays.
He said: “Andreas Christensen is the present and the future for Chelsea.”
Italian reports have suggested Juventus are considering a move for Luiz after Leonardo Bonucci shocked the club by opting to join Serie A rivals AC Milan in the summer.