United are believed to have agreed a €110 million fee for the 23-year-old with the Serie A champions on Thursday.
Real Madrid were also credited with a strong interest in the France international, but the Spanish club's president, Florentino Perez, is said to be unwilling to match the hefty bid lodged by the Red Devils.
Pogba is currently enjoying an off-season break in the United States and it has been suggested he could undergo a medical in Miami, ahead of the transfer being confirmed on the weekend.
The midfielder spent three years in United's youth academy before making the step up to the first team in the 2011/12 season. However, he made just four appearances and went on to join Juve in the summer of 2012 after the expiry of his contract.
Pogba has made 178 appearances for the Old Lady, scoring 34 goals in the process.
Real Madrid's Gareth Bale is currently the world's most expensive footballer, having joined Los Blancos from Tottenham Hotspur in 2013 for a fee of €100m, while teammate Cristiano Ronaldo is in second place after his €94m transfer from United in 2009.