The 27-year-old has failed to establish himself in the way he would have hoped at Juventus, playing just 516 minutes across his 19 Serie A games.
According to Gazzetta dello Sport, West Ham are keen to bring Luiz back to the Premier League and have opened talks with Juventus over a potential deal.
Juventus have slapped a €40 million (£34.5m) price tag on the midfielder but are understood to be willing to negotiate on how the deal is structured.
West Ham are said to want to sign Luiz on an initial loan worth €10 million (£8.6m), with an obligation to buy next year for €25m-30m (£21.6m-25.9m), if certain conditions are met.
Graham Potter’s side are yet to make any move in the summer transfer window other than the signing of Jean-Clair Todibo, who joins permanently from Nice for €40 million following his season-long loan.