The 22-year-old suffered the injury at the beginning of April, but Davis is confident that the Frenchman will return for the start of next season.
Davis told the club's official website: "Mathias suffered a grade two tear in his thigh and he and his agents wanted him to have surgery in Italy with a specialist. We were fine with that and he has had that now.
"He has been over to be checked out by [physio] Rob [Sharp] and he is fine with it. He will return to Italy shortly to undergo more rehab with the surgeon who conducted the operation.
"It is common practice for foreign players, especially in Italy and France, to have surgery for this type of injury. In Britain, we are perhaps more cautious but we were fine with it and Rob has been kept informed.
"Mathias is on a crutch at the moment but we are sure he will be fine and will return for pre-season training on schedule."
Pogba has scored 16 goals for the club this season.