The French youngster joined the Red Devils' youth academy in 2009 from Le Havre but, was unable to force his way into the first team, making just three Premier League appearances.
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"Sir Alex Ferguson tried to keep me at Manchester United, but he didn’t get very far," the 20-year-old told Sky Sport Italia.
"Other clubs were tracking me but I only had Juve in my mind. At the time, I heard from Chelsea, Arsenal and Milan, but nobody is like Juve."
The Bianconeri have seen world-class French midfield players play at the club, including Michel Platini, Didier Deschamps and Zinedine Zidane.
Pogba says having the opportunity to emulate those footballing greats was a key factor behind his decision to move to Turin.
"Since childhood I’ve always liked Juve and supported that team," he added.
"For the French this club means a great deal, as so many French champions played in Turin, so that’s why I liked them.
"I am happy to be here and I want to win many trophies with this jersey."
Pogba has so far won the Supercoppa Italiana twice and Serie A once.