The 19-year-old turned down the offer of a new contract with United and could become Juve's first summer signing.
"I am thinking about my future, I am in Italy with Juventus to discuss my transfer," Pogba wrote on Twitter.
Pogba left Le Havre to join United's youth academy in 2009. He made just three league appearances for the Red Devils last season.
Even if he does sign for Juve, there is talk Pogba won't actually play for coach Antonio Conte and instead will be used as a makeweight in an offer for Udinese midfielder Kwadwo Asamoah, who is also interesting United.