Pogba was provisionally suspended in September after he tested positive for testosterone.
A month later a B sample confirmed the presence of the substance.
Proceedings by the Italian sports justice system are underway while the Turin public prosecutor's office has also started a judicial investigation, as doping is a criminal offence in Italy.
"I can confirm that we received this morning this notification from the anti-doping agency with four years (suspension) requested," the Juve source told AFP.
The 2018 World Cup winner's sample was reportedly taken at his club's opening match of the Serie A season, a win at Udinese on August 20, during which he was an unused substitute.
Pogba's representatives said the testosterone came from a food supplement prescribed by a doctor he consulted in the United States.
Under the World Anti-Doping Code, Pogba is liable to a four-year suspension, which could be halved if he proves that he was not at fault.
The ban could even be limited to a few months if the use of the substance took place "out of competition and is not related to his level of performance".
Since the announcement of his positive test, Pogba has been unable to train with Juventus, the club to which he returned in July 2022 after six seasons with United.
Juve have also suspended payment of his estimated annual salary of €8 million (£6.86 million).
