The City Ground club, who are in the top four this season, want to land the ex-Aston Villa star.
Luiz moved to Juventus in a mega deal this summer but failed to impress in Turin.
According to Relevo, there are many teams that want to sign him away from the Italian giants.
Villa are not interested in bringing him back, but he may have a return route to the Premier League via Forest.
Luiz may find the hustle and bustle of the Premier League more his style than the tactical nature of Serie A.
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