The Italy international's future at the Italian champions has come under speculation following his failure to play regularly this season.
The arrival of Athletic Bilbao forward Fernando Llorente on a free transfer in the summer has also played its part in making things uncertain for Quagliarella, but Beppe Bozzo insists that the 29-year-old is not worried about extra competition.
"Despite all the market rumours, I think that Juventus are convinced of keeping him," he told Tuttomercatoweb.com. "He has shown that he can be counted on, that he always responds every time that he is called upon.
"He's reached the maturity that you need that allows you to continue playing for a great side. The extra competition will be a problem for all Juventus's forwards.
"All are under discussion with Antonio Conte in charge. The coach has done well to rotate his attackers and not assure anyone a starting berth. If new forwards arrive, then that will not be a problem only for Fabio."
Quagliarella's current contract with Juventus runs until the summer of 2015.