The 30-year-old was expected to leave Turin during the summer transfer window following the arrivals of forwards Fernando Llorente and Carlos Tevez.
"Fabio didn't want to leave Juventus," he told TMW. "He simply asked for more space in the side because he knows he can be of use. And boss Antonio Conte has always believed in him.
"Quagliarella received a number of offers from Italy and abroad, but the club decided to keep him because he is part of the project and considered an important player.
"Then it is only normal that you have to accept the rotation policy when you are part of a great side."
Quagliarella, who has 25 caps for his country, joined the Old Lady from Napoli in 2010.