Wales team physiotherapist Mark Davies said: "Ryan will be seeing a specialist on Thursday, and we will know more when we get the results of that consultation.
"Until then, it would be wrong for us to speculate," he added.
Jones' back-row colleague Jonathan Thomas, meanwhile, has returned to training after being told his broken hand will not require surgery or plaster.
He should regain full fitness during the next two or three weeks, and Davies added: "Jonathan has damaged the metatarsal on the ring finger of his left hand.
"Fortunately, the damage is in an area that does not limit his movement or grip to any large extent, and he is able to take a major part in sessions.
"He should recover more quickly than we first thought."
A third injury victim, wing Shane Williams, is expected to join Thomas in being available for selection next month after undergoing elbow surgery.
Davies said: "Shane is in a similar position to Jonathan.
"He is avoiding full contact at the moment, but can still play a major part in the training sessions. The good news is that he should be fully recovered by August."