The 19-year-old arrived in the French capital from Pescara for £8m during the summer transfer window and has already impressed in his short time in Ligue 1.
Baresi, who spent 20 years at the heart of the AC Milan defence, said that Verratti will continue to improve under the tutelage of Carlo Ancelotti.
"He is very young but already very professional and mature," Baresi told French radio station RMC.
"He's going to be very strong. He'll gain experience in Paris, playing with great champions and being trained by Carlo Ancelotti, a very experienced coach.
"He will be important for this club."
Verratti made his debut for the Azzurri in August's 2-1 defeat to England.