The 29-year-old is expected to leave Old Trafford when his contract expires next month, with Juve believed to be the frontrunners to sign the Frenchman as a free agent.
Pogba is understood to have rejected an approach from Premier League leaders Manchester City, and while the likes of Barcelona, Real Madrid and Paris Saint-Germain have also been credited with an interest, a return to Turin now seems to be on the cards for the midfielder.
Speaking to Sky Sports News in Italy about the prospect of Pogba returning to Juventus, Arrivabene said: "He is a Manchester United player. We respect them, and we would have to inform them first due to a gentleman's agreement. He has the same agent as Moise Kean and Luca Pellegrini, so talking is routine. He was not the main topic.
"I agree that we could use a top-notch midfielder, and we are making our evaluations. We need the right balance across every role. The squad has to be financially sustainable, and we want the right combination between youngsters and veterans."
Pogba joined Man United from Juve for around £89m in the summer of 2016 and has since recorded 39 goals and 51 assists in 233 appearances across all competitions.
The France international is not the only player who is set to depart United on a free transfer this summer, as Edinson Cavani, Jesse Lingard, Juan Mata and Nemanja Matic are also out of contract in June.