Journalist Thomas Gibson said in a post on X that Wood had said “hopefully it’s okay”, as he passed through the post-match mixed zone.
Forest also lost defender Murillo and attacking midfielder Callum Hudson-Odoi to injuries during the match, but Wood’s injury appears to be less serious.
“I don’t know, I’m not a doctor,” Pereira said. “I think Chris and Murillo will not be anything significant.
“Chris has a haematoma, but I think they will both be ready for Burnley. For Callum, it’s a muscle injury, which is the bad news.”
All Whites coach Darren Bazeley will definitely be hoping Wood is fit enough to face Burnley, with their first match at the World Cup slated for June 16 against Iran in California.
In a statement, Bazeley said he has been in touch with Wood since the fulltime whistle.
“Myself and our medical team have been in contact with Chris and Nottingham Forest following the game today,” Bazeley said.
“While you obviously never want to see our players go down injured, the impact was on the other knee to where he recently had surgery.
“He will be assessed by Forest, but it doesn’t sound like it is as serious as it first looked, thankfully.”
Before the match, Wood spoke about the long-term impact his knee injury will have on him for the rest of his life.
“It’s a knee injury, it’s going to take years of managing throughout my whole career, and when I’m playing with kids, playing golf or doing whatever I do after football,” Wood said.
“It’s going to be there. I’d say it’s always got to be in your back of mind that I have to keep myself in top shape ready to go.
“A knee injury is always horrible, you never know what could happen in the future or how you are going to come back from it.
“So mentally, that’s one of the tough things to deal with. But I had confidence I was always going to come back. I got very close to returning pre-surgery and it just didn’t happen. That’s just unfortunate.”
Wood played his first minutes for Forest’s Under-21s side last month, where he played the first half, scoring a goal.
He then played a further 45 minutes in the first-leg tie against Porto before coming off the bench for 25 minutes in a 1-1 Premier League draw against Aston Villa.
Along with Iran, the All Whites will face Belgium and Egypt in Group G.
It will be New Zealand’s third appearance at the World Cup, having previously played in 1982 and 2010.
Ben Francis is an Auckland-based reporter for the New Zealand Herald who covers breaking sports news.