Should he fail to recover in time, Sean Cronin will start in the front row alongside Cian Healy and Mike Ross with Damien Varley coming onto the bench.
Head coach Declan Kidney commented: "We have to put a team in 48 hours before kick-off. The decision (on Rory) 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 his 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."
Otherwise the selected team is unchanged from last weekend's 36-6 victory over Italy which confirmed Ireland's presence in the knockout stages of the World Cup.
Keith Earls, who has scored four tries in his last two games, and Ronan O'Gara, who will be making his 116th appearance for Ireland, both feature in a potent back-line.
Donncha O'Callaghan will win his 80th cap for Ireland in the second row, joining pack leader Paul O'Connell who passed the 80-cap mark earlier in the tournament against Australia.
Continuing on that theme, Saturday's quarter-final will mark the 80th time that Brian O'Driscoll has captained Ireland at Test level. He has led the side to 52 wins so far, including six victories over Wales.
It will be cap number 25 for in-form prop Cian Healy who turns 24 on Friday, while Sean O'Brien, who was acknowledged as the Player of Pool C, links up again with Stephen Ferris and Jamie Heaslip in a combative back row unit.
IRELAND Team & Replacements (v Wales, 2011 Rugby World Cup quarter-final, Wellington Regional Stadium, Saturday, October 8, kick-off 6pm local time/6am Irish time):
15 - Rob Kearney (UCD/Leinster)
14 - Tommy Bowe (Ospreys)
12 - Gordon D'Arcy (Lansdowne/Leinster)
11 - Keith Earls (Young Munster/Munster)
10 - Ronan O'Gara (Cork Constitution/Munster)
9 - Conor Murray (Garryowen/Munster)
1 - Cian Healy (Clontarf/Leinster)
2 - Rory Best (Banbridge/Ulster)/Sean Cronin (Leinster)
3 - Mike Ross (Clontarf/Leinster)
4 - Donncha O'Callaghan (Cork Constitution/Munster)
5 - Paul O'Connell (Young Munster/Munster)
6 - Stephen Ferris (Dungannon/Ulster)
7 - Sean O'Brien (Clontarf/Leinster)
8 - Jamie Heaslip (Naas/Leinster)
16 - Sean Cronin (Leinster)/Damien Varley (Garryowen/Munster)
17 - Tom Court (Malone/Ulster)
18 - Donnacha Ryan (Shannon/Munster)
19 - Denis Leamy (Cork Constitution/Munster)
20 - Eoin Reddan (Lansdowne/Leinster)
21 - Jonathan Sexton (St. Mary's College/Leinster)
22 - Andrew Trimble (Ballymena/Ulster)
Follow the Ireland team in New Zealand on www.twitter.com/irfurugby.