The Leinster fly-half, who has been playing at centre in the World Cup, may even be laid low on Friday but the Pumas hope he will be ready for this weekend.
With the game likely to be dominated by the boot, Contepomi is set to have an important role in the game - should he play.
His kicking duel with deadly Scotland marksman Chris Paterson could go a long way to deciding the result.
Argentina will be expected to see off the Scots and progress to their first World Cup semi-final.
They are even being tipped as title contenders after their smooth progress out of a tough-looking Group D, and there is a lot of hype around the Pumas back home.
The football-mad nation has turned rugby crazy, with the Superclasico derby between Boca Juniors and River Plate - arguably the biggest match in soccer - rescheduled so it does not clash with Sunday's match.
Lock Rimas Alvarez Kairelis does not see the hype affecting him and his team-mates, however.
"All the media are saying that but we are trying not to think that way," he said.
"We're going into this Scotland match the same way we started against France and Ireland.
"Getting to the quarter-finals is like a dream for us. We know now that we have a big chance.
"It's the first time for an Argentina team to have this chance and we are taking it very seriously.
"We can't believe we have achieved this."
Argentina are above Frank Hadden's men in the world rankings, and are undefeated against the men in blue since 1990.
But the Pumas are continuing to play down their chances.
Toulouse prop Omar Hasan said: "Despite what the rankings say, we are at the same level and we are not any better than them.
"Scotland have a line-out as good as Ireland's, and (Chris) Paterson has a cannon in his leg, so we must not relax for a second.
"The team has matured and they apply the experience they have gained."