The Bianconeri won three Scudetti in a row and dominated Italian football under Conte but, following the coach's resignation in July over frequent disagreements with the board, Allegri was handed the reins in Turin.
Pogba, brought to Serie A from Manchester United two years ago, is one of Juve's prize assets and stamped his authority on the first team last season but his new coach says that the French midfielder will be ushered into a more forward-minded role in 2014-15.
"I will try to use Pogba more in attack," Allegri told reporters in Indonesia as Juventus embark on a tour of South East Asia.
"He is one of the best young players in the world, with enormous technical and physical qualities. Having said that, there is also still plenty of room for improvement."
Pogba and fellow Juventus midfielder Arturo Vidal have been persistently linked with a transfer away from Italy this summer but Allegri says that both are content with life in Turin.
"Vidal and Pogba are delighted to be here and I am delighted to coach them," the former AC Milan boss declared.
Pogba, who claims that he has no plans to leave the reigning Italian champions, was equally gushing with praise for his new boss and says that Juventus have adjusted to life without Conte with ease.
"Conte and Allegri are two of the best coaches around and the atmosphere was immediately pretty good," the France international observed. "We are motivated and ready to work successfully with Allegri. Conte's gone and now we have Allegri - we are ready to work together in absolute harmony.
"I am very happy to play for Juve. I am just focused on playing right now; the future does not concern me, I live in the present.
"I am not thinking of my contract and do not have meetings scheduled with Juventus chiefs. My goal is to continue to do well on the pitch."