La Stampa daily said the 22-year-old is involved in a criminal probe targeting users of illegal online betting platforms, along with other unnamed suspects.
"I confirm the news of the investigation," Turin Chief Prosecutor Enrica Gabetta said in an emailed statement, without elaborating.
Turin is the home city of Juventus, the former Italian champions.
"Our client is dealing with the matter responsibly, with a view to maximum transparency and collaboration with the ordinary and sporting judicial authorities," Fagioli's lawyers Luca Ferrari and Armando Simbari said in a joint statement.
"Nicolo is calm and fully focused on Juventus and the [Italian Serie A] league," they added.
The newspaper did not say what kind of betting Fagioli was involved in. Italian football authorities ban players from betting on matches but not from other types of gambling.
The prosecutor's office of the Italian football federation (FIGC) is also looking into Fagioli's case, a source close to the matter said, confirming another part of the La Stampa report.
A player found to have bet on football matches risks being disqualified for at least three years and fined at least €25,000 ($26,517.50) under the FIGC's code of conduct.
Juventus declined to comment on the affair. Attempts to reach Fagioli via social media messages were not immediately successful.
Fagioli has played in six of Juve's eight Serie A matches this season. Last November he made his debut for Italy, coming on as a substitute in a 3-1 away friendly win against Albania.