The Brazil international has just 12 months remaining on his contract and Villa will consider offers as they look to avoid losing him for nothing next year.
Reports in Italy over the weekend claimed Roma, managed by former Chelsea and Manchester United boss Jose Mourinho, remain interested despite having already signed Nemanja Matic on a free transfer.
Luiz has been a first-team regular since joining Villa from Manchester City for £15million in 2019, starting 34 matches last season.
But the arrival of Boubacar Kamara from Marseille means he will face an increasing battle for playing time next term.
Luiz’s future is one of several likely to be settled during the current transfer window as boss Steven Gerrard reshapes his squad.
Trabzonspor are in talks over a permanent deal for Trezeguet while fellow winger Bertrand Traore is also receiving interest from Europe.
Traore made only nine Premier League appearances during an injury-ravaged second season at Villa Park and Gerrard will decide whether to give the Burkina Faso international another chance to impress.