Best has been named in the starting-line-up for Saturday's showdown at Wellington Regional Stadium and will be given as much time as possible to prove his fitness.
The Ulster hooker sustained a sprain to his right shoulder during Sunday's 36-6 victory over Italy and has been receiving intensive treatment since.
Under World Cup regulations the deadline for teams to be submitted is 48 hours before kick-off, meaning head coach Declan Kidney has until 6am BST on Thursday to confirm his selection.
If Best continues to heal swiftly it is unlikely he will be withdrawn with his battle for fitness certain to continue to matchday.
"The decision could go right to the end, we'll make it when we have to make it," said Kidney.
"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."
Best's outstanding form as part of a highly impressive Ireland front row is compelling Kidney to do everything possible to ensure his inclusion.
Should he fail to pull through, Sean Cronin will be promoted to the starting line-up with Damien Varley appearing on the bench.
Kidney has named an unchanged side to face Wales with Ronan O'Gara and Conor Murray continuing at half-back.
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