Shaw was carried from the field when he landed awkwardly at the lineout, although scans later revealed soft tissue damage, rather than a break.
While Wasps have refused to speculate on when he might return to action, in a statement they offered Ashton hope that he may at least be able to play some role in the tournament - which England begin with a Twickenham clash against Wales on February 2.
"Simon Shaw is recovering remarkably well from his ankle injury," the statement said.
"He is walking well without the assistance of crutches, and though it is too early to recommend a timescale for his return to playing, the signs are very encouraging.
"He will continue intensive rehab with the club throughout this week."