Davies' regional team the Scarlets have said that he is "progressing well" from the pectoral muscle injury he suffered during Wales' opening autumn Test against South Africa in November and has resumed light running.
But they do not expect the 25-year-old Davies, a star of last summer's successful British and Irish Lions tour of Australia, to be back playing until early March.
That scenario would sideline him from reigning Six Nations champions Wales' first three games against Italy, Ireland and France, while he would have hardly any time to prove his fitness before appointments with England on March 9 and Scotland six days later.
The Scarlets, meanwhile, believe that Davies' fellow internationals Liam Williams and Ken Owens each face three-week absences after suffering respective finger and ankle injuries during a Boxing Day defeat against the Ospreys.
The Llanelli-based region have also confirmed that their wing Mike Poole is continuing his recovery in a Cardiff hospital after undergoing surgery to stabilise a serious neck injury suffered during a Welsh Premiership game between Llanelli and Swansea five days ago.
Poole, 27, underwent two operations following a fracture and dislocation to his neck. He was initially taken to Swansea's Morriston Hospital, and then transferred to Cardiff.
Scarlets' medical chief Andy Walker said: "Mike's injury was serious.
"The surgery undertaken has been successful, and thankfully there has been no loss of function as a result of the injury.
"He will undergo a further CT scan later to ascertain whether he will need one further operation. However, to date, he has progressed well, the injury has been stabilised and he is recovering."
And Scarlets head coach Simon Easterby added: "Everyone at the Scarlets, and especially the coaches and all our players, send Mike and his family their very best wishes.
"We have been in close contact with the hospital teams, Mike and his family throughout, and we are all pleased to see him making good progress."
- Sports & Recreation
- Disease & Medical Conditions
- Mike Poole