The 20-year-old says he hopes to aspire to the level the legendary Frenchman was at during his career, 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.
He told Corriere dello Sport: "I had a year with this club and am very happy because we won the Scudetto.
"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 Under-20 World Cup this summer, went on to state Andrea Pirlo was the modern-day player whom he hopes to follow the example of.
He added: "Certainly Pirlo! I hope I can do what he is able to do one day."
The Frenchman, whose contract with the Italian giants runs until June 2016, featured 27 times last season for Antonio Conte's men scoring five goals.