The Red Devils have reportedly lodged a bid worth around £100m, including add-ons and performance related bonuses, but the Old Lady are determined to hold on to their prized asset for at least one more season.
However, it has been suggested that the defending Serie A champions would be willing to allow Pogba move if United make an improved offer.
Pogba's agent, Mino Raiola, has already facilitated the transfers of Zlatan Ibrahimovic and Henrikh Mkhitaryan to Manchester United, and has told Juventus chiefs that he intends to help the Frenchman seal a return to the English Premier League.
Real Madrid are also keen on signing Pogba, but are not willing to meet Juventus' steep asking price, while their manager, Zinedine Zidane, has hinted that Los Blancos will not rival United for the player's signature.
When asked about Real's reported interest in Pogba, Zidane said: "Do I like Pogba? Of course, he's a very good player and every club wants the best players but right now he's at Juve and we have a large squad already.
"There are still lots of players yet to join up with the squad and with the Euros going on we couldn't do anything. We have three games coming up and that's the focus at the moment."
Pogba, 23, left Old Trafford back in 2012 after rejecting a new contract. He has gone on to make 124 appearances for Juventus, scoring 28 goals in the process.