Luiz sparked controversy this week when responding to one fan on social media complaining about the lack of games he's played this season.
The Brazil midfielder defended his record, bringing into question the way he had been treated by former coach Thiago Motta, along with the injuries he suffered this term.
Now Juventus is considering taking action, says La Gazzetta dello Sport.
The outburst could lead to disciplinary consequences for the Brazilian, including a heavy fine for violating the club's code of ethics.
Luiz stated this week: “I didn’t come here just to take pictures; nobody else did. I want things to be different. I came with a purpose, I listened to my heart when I signed. Now, I want you to answer me: why hasn’t a signing like me played two consecutive matches with this shirt?
“You can say whatever you want to the press later: ‘Douglas isn’t fit.’ Am I not fit? I did the entire pre-season and played every match.
“I had come off one of the best seasons of my career, one of the best defensive midfielders in the Premier League. Injuries held me back. True.
“But how long did I stay on the bench while I was fit? A lot. These injuries were not normal. I’ve never been injury-prone, but there are many reasons that could have caused this, which I’d rather not comment on. I will keep giving everything for this club, even though it’s hard sometimes. It’s not easy, but you can count on me.”