The Chilean has caught the eye during a positive season for Udinese, with the likes of Internazionale, Milan and Deportivo La Coruna all credited with interest.
Marcello Lippi`s Juve are the latest team to be mentioned in connection with a summer move, and Pizarro says it would be fantastic to play for the Turin outfit.
"I am living a dream but if I have to go to Turin I would be in paradise," said Pizarro.
"I feel very proud that Juventus have shown interest in me but I am a person that doesn't get drawn just like that.
"I have a contract until 2005 with Udinese and I feel very comfortable here.
"If destiny says that my future is in another place and my family agrees, I will follow that but those things must be handled by my agent and the club."
Veteran Argentine defender Nestor Sensini feels Udinese would suffer if they lost the 23-year-old.
Sensini said: "It's difficult to find players with the talent that Pizarro has, not only because of his quality, but also he makes lots of sacrifices for the team and runs a lot.
"He is showing all his value and he is very important for our team.
"Pizarro is a very good player and could play in any Italian team."
