Davies missed the start of the season with a foot injury and played just four games before suffering a setback.
The Wales star has undergone further treatment during the international break and should rejoin his team-mates next week.
"I hope I'll be able to start running over the weekend and crack on with training next week," he told his club's official website. "If all goes to plan I should be back and available by the end of the month.
"I hope I'll only miss two or three games at the most. It's been frustrating - but it's just one of those things."