The Alex have been without the 23-year-old since April, first because of a thigh problem and then due to a knee injury sustained in the friendly with Manchester United which required surgery.
Boss Steve Davis originally feared he could be without Pogba until December, but he is now more optimistic when trying to quantify a return date.
"He is looking forward to getting back," Davis told Crewe's official website.
"He will be extremely frustrated with his injury and the timing of it but he has always got a smile on his face.
"Rob (Sharp, head physio) has got a great record of bringing players back early and he is way in to his rehabilitation now.
"It is too early to put a date on a return. It is normally two steps forward, one back with an injury like that and it depends on the mentality of the player. Knowing Mathias he will be back earlier than expected."
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