The 20-year-old Juve starlet says he aspires to be at the level of the legendary Frenchmen, while noting Andrea Pirlo is his modern-day hero.
The France international has emerged as one of the continent's finest youngsters following a promising first season in Italy - which resulted in a Scudetto - after his move from Manchester United last summer.
Zidane won two league titles throughout a five-year spell with the Italian giants before departing for Real Madrid in 2001, and Pogba has revealed he hopes to leave his mark on the club.
"I had a year with this club and am very happy because we won the Scudetto," Pogba told Corriere dello Sport. "I hope to become as big as Zidane, Lillian Thuram and Didier Deschamps, but I have to work hard to reach their level."
Pogba, who won the FIFA Under-20 World Cup with France this summer, went on to state Andrea Pirlo was the modern-day player who sets the example for him to follow.
"Certainly Pirlo! I hope I can do what he is able to do one day," Pogba said.
Pogba, whose contract with the Italian giant runs until June 2016, featured 27 times last season for Antonio Conte's men, scoring five goals.