Luiz only joined Juve from Aston Villa last summer but has struggled to find a place in coach Thiago Motta's squad.
La Gazzetta dello Sport says that West Ham United and Fulham have joined the search for the Brazilian midfielder.
West Ham have already made an initial investigation into the player.
Juve chief Cristiano Giuntoli met with Manchester United and Manchester City officials a fortnight ago to offer them Luiz before the January market.
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