Pogba inspired France to success at the 2018 World Cup, but the midfielder's form at United has been inconsistent, and he continues to be linked with a move away from Old Trafford.
Barcelona are believed to have had a swap bid rejected for the 25-year-old, but it is understood that the Red Devils will have to fight off another bid ahead of Thursday's transfer deadline.
According to Mundo Deportivo, Juventus are desperate to re-sign the World Cup winner this summer, and the Italian champions will offer United the chance to sign highly-rated midfielder Pjanic as part of the deal.
Pjanic joined Juventus from Roma in the summer of 2016, and has scored 15 times in 91 appearances for the Italian champions over the last two seasons.
The 28-year-old, who has also been linked with Manchester City, said last month that he would not be leaving the Old Lady ahead of the new campaign.