Pogba, who joined the Red Devils’ youth academy in 2009, spent three years at Old Trafford, yet made just three senior appearances before signing for current Serie A club Juventus.
And Ferdinand, who saw the Frenchman’s undeniable talent in training while at United, backs the 21-year-old to become one of the best in his position.
"Paul told me before he left that he wanted to be 'the best player in the world,'" the former England international told BBC Sport.
"I don't know whether that will happen, but he will definitely turn out to be the best midfielder in the world.
"As well as his undoubted ability, his strength is definitely his self-belief, not just by statements like that but by how he backs them up.”
Ferdinand also lauded the youngster’s mental strength after making the move away from England.
"He made the big, bold move to leave United, the best club in the world in my eyes, at only 19 because he wanted opportunities,” said Ferdinand.
“He backed himself to do it, which is a big thing to do for a kid of his age, and he has not looked back since.
"You have to have that arrogance about you as a young player coming through at United, otherwise you sink. You won't make it."
Pogba has been in stellar form for Les Bleus, scoring his first goal in his maiden World Cup tournament in his side’s 2-0 win over Nigeria on Monday.
Pogba and his charges next face Germany in their quarter-final match-up on Friday in Rio de Janeiro.