The lock has missed Wales’ opening two matches of the competition – a 33-7 thrashing of Italy and a narrow 21-16 defeat to England – with a fractured hand.
It was initially thought Charteris would be fit in time to face the defending champions in Cardiff last Saturday, but he was forced to sit out as Elliot Daly’s late try kept Eddie Jones’ men on course for a second successive Grand Slam.
Jake Ball has partnered captain Alun Wyn Jones in the second row in Charteris’ absence, but interim head coach Rob Howley may have a tough decision to make when his side head to Edinburgh for the clash on February 25.
“Luke is back up and running,” said forwards coach Robin McBryde in a media conference on Thursday. “He has done a bit of passing today, albeit he has still got a bit of protection on his hand.
“So everything is going in the right direction and it’s just step by step with him with regards to how we increase his load.
“If you ask Luke, he will be fit to play. I am not sure about the medics yet.
“He has had that little bit of extra time to heal his hand. Obviously he picked up a hamstring injury as well.”
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