The Turin Prosecutor's Office is looking into the 22-year-old's alleged activity on unauthorised online gambling platforms, according to Tuttosport.
The Italy international's lawyer says that Fagioli reported himself to the sports justice system and that he is calm about the situation.
However, if found guilty of the allegations, he could face around three years out of the game.
"Nicolo is calm and is fully concentrated on Juventus and the championship," his lawyer said. "In our quality of Nicolo Fagioli's lawyers, in reference to the news that appeared in the press today, we can represent that our client is dealing with the matter responsibly, with a view to maximum transparency and collaboration with the ordinary and sporting judicial authorities, as demonstrated by the fact that he was the first to act promptly and promptly towards the Federal Prosecutor's Office."
Fagioli has already been questioned by the Italian Football Federation (FIGC) about the matter. Prosecutors are said to have opened the investigation at the end of August, meaning the case could be resolved by November.
The case arose when investigators looked into transactions of gambling websites operating without a license and discovered Fagioli's name. Such offences usually result in a fine, but as Fagioli is a professional sportsman who is a member of a federation, the punishment may be heavier.
The news will come as a concern to Juventus, who are already without midfielder Paul Pogba, who faces a lengthy suspension after testing positive for a banned substance.
Fagioli has been a regular part of Allegri's team this season, having featured six Serie A matches and earned a cap for Italy.
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