Best sprained the AC joint on his right shoulder in last weekend's victory over Italy, but the injury has responded well to treatment.
The Ulster hooker, who has been in superb form throughout the World Cup, has been named in the XV with Sean Cronin on standby to start in the quarter-finals if he fails to recover.
"We have to put a team in 48 hours before kick-off," said head coach Declan Kidney.
"The decision could go right to the end, we'll make it when we have to make it.
"I wouldn't want to tempt fate by rating Rory's chances, but he's not ruled out which is always the first sign.
"He had a good day yesterday which everyone was very positive about. He's making great progress and we're taking it one day at a time."
If Cronin is drafted into the starting line-up, Damien Varley will be promoted to the bench.
Unsurprisingly, Kidney has retained half-backs Ronan O'Gara and Conor Murray after they impressed in the 36-6 thumping of Italy at Otago Stadium.
Once more Jonathan Sexton and Eoin Reddan have been confined to the bench.
"Half-back is the most competitive area of the team. I know it's unconventional to use different half-backs at different times," said Kidney.
"When they've been on the pitch they've brought their own things to it.
"For example Jonathan was hugely strong for us in defence in the last 10 minutes against Italy.
"Eoin robbed two great balls for us in the last 10-15 minutes.
"Leaving them out isn't easy, but Conor and Ronan have gone quite well for us."
Kidney swatted aside concerns that Wales will target O'Gara's defensive frailties, as they have done in the past under coach Warren Gatland.
"They have quite an array of places where they can attack, I don't think they'll pick anyone in particular," he said.
"Wales are a better side now because before you knew where they would attack, but now they attack other places too.
"It's going to be a case of everyone defending their own zone."
Team selection will have posed Kidney and his assistants few problems given Ireland's emphatic performance against Italy.
The only area of doubt is on the wing where Andrew Trimble is pushing Keith Earls hard for the number 11 jersey.
Ireland start as marginal favourites against Wales, who they have beaten in nine of the last 12 meetings, but the outcome of Saturday's first quarter-final is impossible to predict.
"Playing Wales is a huge challenge. They got the better of us in March and are going well," said Kidney.
"They only lost to the kick of a ball against South Africa, otherwise they'd be on four wins from four games.
"They beat England and Argentina during the warm up games as well.
"They have a few younger players who have brought their own spark. The senior guys are showing good form too.
"They're showing different trends in the way they play, but are more unpredictable than before.
"If it was possible to read them before, it's more difficult now."
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