The Frenchman opened the scoring in Sunday's 3-1 win over Napoli and has been one of his Juve's key performers this term as the champions target a fourth consecutive Scudetto.
After an impressive showing for Juve at the Stadio San Paolo, Allegri sees no reason why he cannot achieve similar feats to those of France greats Zidane and Platini.
Zidane won world and European honours on the international stage, with Platini also claiming the latter prize, and both earned two Serie A titles in Turin.
Zidane was twice a UEFA Champions League runner-up with Juve, while Platini was a European Cup winner in 1985, and Allegri feels that Pogba can follow in their footsteps.
"I hope that Pogba is able to come close to achieving what Zidane and Platini achieved at Juventus," the Juve coach said of the 21-year-old who already has two Scudettos to his name.
"He is still very young, and has all the quality to do so.
"He scored a wonderful goal [against Napoli] and played reasonably well after the goal, but I think he has the quality to do much better."
Juve are three points clear at the summit of the table and face a last-16 tie against Borussia Dortmund in the Champions League.
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