The Hammers centre-back got through the full 90 minutes as the All Whites kept a clean sheet in goalless first leg at the Westpac Stadium in Wellington on Saturday.
New Zealand coach Anthony Hudson is confident his skipper will have no problem starting the second leg in Lima.
“It wasn’t muscular, it was just a knock,” he said.
“This morning we’ve had a good recovery session, we’ve had a good session with the subs. Now what we need to do in the next couple of days is make sure we do everything possible to get our best team on the pitch.”
Reid was satisfied with his, and his team’s, performance on Saturday.
“We’ve been close to getting a result before against the so-called bigger teams,” the Hammers defender told Fox Sports.
“Today, for me, was about keeping a clean sheet at the back and giving ourselves an opportunity in the second leg. We’ve certainly done that.”
Arsenal are lining up a move to bring Sevilla midfielder Steven Nzonzi back to the Premier League this summer.
Tottenham are reported to have been offered Lyon playmaker Nabil Fekir following the collapse of his move to Liverpool.
Manchester United are ready to launch a straight £60million bid to try and sign Chelsea star Willian, reports have claimed.
Liverpool are being linked with a swoop for Inter Milan striker Andrea Pinamonti, but have been warned he wants regular action.
Borussia Dortmund are reported to have dropped all interest in Chelsea striker Michy Batshuayi and are looking elsewhere.
Sevilla are bracing themselves for interest in Steven Nzonzi and have lined up a replacement in the form of Marcos Llorente.