The centre-back picked up a knock in Wednesday’s 7-1 Champions League defeat by Liverpool and was originally a doubt for Sunday’s cinch Premiership match against Motherwell at Fir Park.
However, the 27-year-old’s condition is not believed to be as serious as first feared, according to reports, and he may be able to take his place in Giovanni van Bronckhorst’s defence against the Steelmen.
Davies’ inclusion would be a welcome bonus given that the Gers manager is facing a mounting injury crisis.
Both defender Connor Goldson and midfielder Ryan Jack have been added to the injury list after being forced off against Liverpool.
Goldson’s fellow centre-backs and Filip Helander and John Souttar are still out, along with Tom Lawrence and Ianis Hagi.
Motherwell manager Steven Hammell will make some late decisions on his team to face Rangers.
Blair Spittal went off with a knock against Hibs last weekend while Callum Slattery’s involvement is also unclear.
Connor Shields is suspended following his red card at Easter Road while Rolando Aarons (hamstring) remains on the sidelines along with long-term absentees Jake Carroll and Nathan McGinley.