The 23-year-old defensive midfielder has missed the last three games because of a hamstring injury and is expected to return to the team once he recovers.
Steven Gerrard is now in charge of the club and the Aston Villa boss is believed to be counting on the Brazilian, but it has been claimed that the midfielder is feeling unsettled at the club.
Luiz is said to have rejected offers of a new deal from Villa with little over 18 months left on his current contract.
And according to Italian outlet Il Romanista, his agent will be scouring Europe in December ahead of the winter transfer window.
It has been claimed that the midfielder’s agent will be looking to attract interest from clubs before going back to Aston Villa with offers for Luiz in the winter transfer window.
Roma are believed to be interested in signing the midfielder but his cost is expected to be prohibitive in January.
Aston Villa are only expected to sell Luiz in the middle of the season if they receive a fee in the region of €35m.
It has been claimed that Roma could wait until the summer to make a move for the Brazilian midfielder.