Inter confirmed the arrival of Gagliardini from Atalanta on Wednesday, initially on loan until the end of next season but with an obligation to make the move permanent.
The 22-year-old has only played 14 games in Serie A but was included in Giampiero Ventura's Italy squad for the recent matches against Liechtenstein and Germany, though he failed to make his international debut.
Gagliardini idolised Real Madrid boss Zidane when he was growing up but now looks to another Frenchman in Pogba, who broke the world transfer record when he swapped Juventus for Manchester United in August, for inspiration.
"When I was little I liked Zidane, although I did not have the same qualities as him," Gagliardini said on Inter Channel.
"Of today's players, my role model is Paul Pogba – he is the number one in his role."
When asked which Inter player he considered a role model, the 22-year-old responded: "Who else but Javier Zanetti?
"He played for the club for over 20 years. He was always on top of his game. It would be a dream for me [to follow suit]."