The former Welsh captain has an ongoing calf muscle problem that ruled him out of contention for Sunday's Pool D clash against world champions South Africa.
And it has emerged that back-row forward Jones is also likely to be unavailable for Wales' next two group fixtures after the Springboks, against Samoa and Namibia.
Wales conclude the pool phase against Fiji, ahead of a potential quarter-final in Wellington a week later.
Wales assistant coach Robin McBryde said: "Unfortunately, Ryan missed out on the last World Cup.
"The medical staff are telling us he could be fit, if all goes well, for the Fiji match.
"We will wait and see after the weekend where we stand injury-wise.
"He does have a realistic opportunity, at this stage, of taking part in the World Cup.
"He spoke to the group this morning, and he spoke very well.
"It's tough for him at the moment, but everyone is doing their best to put their arm around him and keep him going.
"He is showing true grit. All the players can take a leaf out of his book."
Wales coach Warren Gatland will need to make a decision at some stage whether or not he keeps 53 times-capped Jones with the squad or summons a replacement.
Leading candidates to take over from the 30-year-old would include Scarlets forward Josh Turnbull and former Gloucester skipper Gareth Delve, who currently plays Super Rugby with Melbourne Rebels.
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