The Manchester United midfielder was in Turin to clean out his locker and hand gifts to players and staff.
After learning of Pogba's performance in victory over Leicester City, Allegri said: “I saw Paul, he was very happy with the choice he had made. Let's say the air of Turin did him good, maybe that's why he came back!
“Pogba is a universal player who can be in a two-man midfield, he can play wide, behind the strikers, even as a support forward.
"He can do anything."