Shane Williams could return to the Wales side for their final World Cup Pool D clash against Fiji on Sunday.
However, James Hook and Dan Lydiate will remain sidelined until a potential quarter-final clash with Ireland in Wellington on October 8.
Ospreys wing Williams missed his side's crushing 81-7 victory over Namibia on Monday with a thigh strain but his recovery is going well and he is nearly back to match fitness.
"Shane is recovering well," Welsh Rugby Union national medical performance manager Prav Mathema said.
"He is back up and running and we are pleased with his progress, but the next 48 hours will be essential in determining whether he may be available to us this weekend."
Flanker Lydiate injured his ankle during the 17-10 win over Samoa on September 18 and will miss a second straight game due to the problem.
"Dan is now back running again after suffering an ankle ligament strain in the Samoa game," Mathema added.
"He has been incredibly diligent with his rehab and his self-management, and as a consequence has given himself every opportunity to be available for selection within the next two weeks.
"He still has a number of stages to complete within his rehabilitation but we are confident that he will continue to make a swift recovery."
Hook picked up a shoulder injury in the clash with Samoa and still needs to wait before he gets back in full training.
Mathema said: "James has also been extremely thorough with his rehabilitation and is recovering well from the A/C joint injury to his shoulder.
"We are hoping to integrate him into full training towards the start of next week."