But, as expected, full-back James Hook and flanker Dan Lydiate will not return before a potential quarter-final appointment with Ireland in Wellington on October 8.
Ospreys wing Williams, who missed his side's 81 - 7 victory over Namibia in New Plymouth on Monday with a thigh strain, is at the running stage of his rehabilitation.
"Shane is recovering well," said Welsh Rugby Union national medical performance manager Prav Mathema.
"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."
Dragons back row Lydiate, who injured his ankle during Wales' 17-10 win over Samoa, remains on target to return in the next fortnight.
"Dan is now back running again after suffering an ankle ligament strain in the Samoa game," added Mathema.
"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 also injured his shoulder in the Samoa match, and he is progressing at a similar rate to Lydiate.
"James has also been extremely thorough with his rehabilitation and is recovering well from the A/C joint injury to his shoulder," added Mathema.
"We are hoping to integrate him into full training towards the start of next week."
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