But forwards coach Robin McBryde revealed Jones could need at least a week to recover - and that leaves him in jeopardy for the potential winner-takes-all showdown next Saturday.
At stake is a place in the World Cup quarter-final and a probable clash with South Africa.
If Jones is not fit Wales have more than adequate cover in Chris Horsman, a powerful tight-head prop who is determined to cement his place in the front row.
Horsman and Wales raced to a comprehensive 72-18 victory over Japan on Thursday but can expect a much more physical test from the Fijians.
And the islanders will be fresh after taking the tactical decision to make 11 changes and field a second string in Sunday's Pool B game against Australia.
Japan scored two tries on Thursday from a turnover and an interception and Fiji are even more dangerous playing on the counter-attack.
But the win on Thursday has raised the confidence levels in the camp after a stuttering start to the campaign and James Hook, one of Wales' standout players against Japan, is convinced they can produce a repeat performance.
"It is a huge game in Nantes against Fiji. If we win that we are in the quarter-finals," said Hook.
"If we play the way we played against Japan it shouldn't be a problem - so we have just got to take that over to Nantes.
"This was our best performance for a while. Everything clicked and hopefully we can take it into the next game.
"We are the type of team that when we get quick ball we are superb in attack.
"You have got to be happy with 11 tries at the World Cup. There could have been a lot more tries as well.
"We know we can't afford to let teams like Fiji into the game with intercept tries but also we can't shy away from the [high risk, high reward] way we play the game.
"We scored 11 tries against Japan playing that way. We will not change it against Fiji or any other team."