The 20-year-old Colombian, who has been in impressive form for the Italian club this season, has been linked with Inter Milan, AC Milan and Fiorentina.
"Everyone knew about his qualities, the question was regarding how quickly he would adapt to Italy," Riccardo Calleri told Tuttomercatoweb.com.
"A player with his ability was always going to settle. When you are a champion, you are a champion anywhere.
"His future? I can say that the most important clubs are and will be interested in signing him. He has various offers already, but the decision will be made by Pescara."
Quintero joined Pescara last summer.