The winger suffered a knee ligament injury at Fulham on January 31 Ã¢â‚¬â€œ a real blow as it was his comeback match from the same injury sustained at Middlesbrough on December 18.
Hossam Ghaly is also stepping up his recovery from a groin problem and reserve team top scorer and recent first team squad member Lee Barnard has started running again after his foot sprain.
"Andy Reid is coming back to full fitness and he looks better than ever," said Martin. "I asked him and he had no complaints about his injury.
"He did everything in training on Tuesday so I think he will be fine. Hossam Ghaly was also training and he'll continue building up his fitness."
Martin Jol reports that Andy Reid has returned to training this week after over a month on the sidelines.