Davies had been expected to be recuperating until the New Year, but will return to training next week ahead of schedule.
Villa boss Martin O'Neill confirmed: "Curtis has had some really good news. He saw the specialist and he has given him the OK to train.
"It is one of those injuries where you wouldn't have been tempted to rush anyone back but he has been doing very well.
"The original time frame was about 16 weeks but Curtis is the sort of person who is always determined to come back ahead of schedule.
"I think the specialist is pretty pleased, and so are the physios here who have worked very hard with him.
"He was ill for a couple of days last week but, with a wee bit of luck, should join in with us training-wise next week."
Davies made the £10million switch from West Brom two years ago after initially spending a season on loan and formed an effective partnership with Martin Laursen.
But he will face a battle to regain his first-team spot with O'Neill having signed Richard Dunne and James Collins in the summer, while Carlos Cuellar has impressed this season.
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