The former skipper could be ruled out the tournament in New Zealand before a game has even been played due to a calf injury.
The Wales medical team were monitoring the injury, although with Jones facing at least two weeks out, he could now be replaced in the squad.
And Wales coach Warren Gatland will now wait until the opening game against South Africa before making a final decision.
"We just want to see how Sunday goes and hopefully we won't pick up any injuries and we've just got to give it a little bit more time to settle," Gatland said.
"It's a long tournament and we've got to make sure we make the right decision there. Obviously, if we pick up injuries on Sunday that's going to change our thinking, so we have to see what happens.
"The thing is if we do replace him and if he does recover in two weeks and we pick up another injury, you can't recall that player."
If Jones is ruled out the tournament, it would be the second successive World Cup ended prematurely for the Ospreys ace.
Jones was forced to withdraw from the squad in 2007 with a shoulder injury, while he had missed out on selection four years before.
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