Lock Adam Beard is set to return to full training and could feature in Wales' final World Cup Pool D match against Uruguay next Sunday.
Beard, 23, missed the wins over Georgia and Australia as he recovered from an operation to remove his appendix.
But Wednesday's game against Fiji is likely to come too soon.
"He's been working hard, doing some extra weights sessions as well and he's rehabbed well," said Wales' head of physical performance, Paul Stridgeon.
"He's back into full training this week so he's done well."
Beard's return is a timely one for Wales, who had already lost one second row at the World Cup after Cory Hill had to fly home following his failure to recover from a fractured leg.
Bradley Davies was added to the squad in Hill's place, but before the 32-year-old joined the 31-man party Wales' options looked limited at lock.
Captain Alun Wyn Jones and Jake Ball have been their only available specialist second rows to date in Japan, so Beard's return would be particularly welcome with Wales expected to make wholesale changes to their team to face Uruguay.
Beard has had to play catch-up after having his appendix removed, a procedure which meant he was unable to join the Wales squad when they first flew out to Japan last month.
It also meant he lost a significant amount of weight, which he has been trying to restore by eating more food than usual and adapting his training plan.
"Beardy had that operation which was unfortunate and then he lost three or four kilos," said Stridgeon.
"He's a great kid who does everything we ask, as do all the players, so we've just been getting as much food into him as we can, some supplementation.
"He might be a couple of kilos down on what he was before but that won't affect him in the game."
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