The 25-year-old has been out of action since suffering the problem during a pre-season friendly against Real Betis, but the midfielder has returned to training.
Antolin Alcaraz is also still on the sidelines as he continues to recover from a hernia operation.
"Darron and Antolin are in training with the first team," Martinez said in a press conference. "Now it is a case of getting the match fitness. That could take a couple of weeks, depending on how they react.
"Darron and Antolin won't be fit for the weekend but they are not going to be too far away. For Darron, in a couple of weeks, he'll be getting really close."