The 21-year-old central midfielder joined Man City two years ago in a deal worth £10.8million from Brazilian side Vasco de Gama but has spent the last two seasons out on loan with Girona.
The report claims that Villa are confident of getting a work permit for Luiz and of wrapping the deal up within days.
It is also claimed that Man City have inserted a buy-back clause into the deal.
Man City are set to turn a decent profit on Luiz, a player who has never turned out for the club. He spent two seasons in La Liga with Girona but saw them relegated back to La Liga 2 after their first stint in the top flight – two seasons that coincided with Luiz’s time with the Spanish side. Girona finished 10th in Luiz’s first season but his final game there ended in bitter disappointment. It could have been different for Luiz at Man City had he not been refused a work permit last summer, with Guardiola seeing him as a deputy for Fernandinho – a position they struggled to cover last season. The deal will be of interest to Leeds fans too, with Villa linked with their defensive midfielder Kalvin Phillips. Leeds were asking for £30million and it looks like that could have forced Dean Smith to look elsewhere. There’s no confirmation that this deal will signal the end of their interest in Phillips, but it will make the Leeds fans feel a whole lot more confident that Phillips will be at their club at the start of next season.