Luiz has made just four appearances in 2018
The Brazilian fell out of favour at Stamford Bridge last season under Antonio Conte and made just four appearances in 2018.
The 31-year-old is now considering his options and a return to Benfica has been mooted.
The Italian is said to be a big fan of the centre-back and he has added him to his summer shopping list.
As well as Luiz, Ancelotti is hoping to bring in Bayern Munich midfielder Arturo Vidal.