England are seeking a replacement for James Anderson, whose tour has ended after he picked up a rib injury in the 189-run second test victory in Cape Town.
Archer missed that game with an elbow problem and Wood has had a number of fitness issues in the past, meaning neither might get the nod.
"No decision has been made," Root told reporters. "It is important to use today's training session to get a real clear understanding of where everybody is at and as this tour has proven, make sure that we are all ready to go when we turn up to play."
Root suggested a fully fit Archer would play, but whether his elbow will hold up over five days, allowing him to bowl at his full intensity, is the big question.
"With Jofra, he is 24-years-old, right at the start of his test career and has a huge amount of ability. It is clear to see what he is capable of doing," Root said.
"But managing workloads is a very important part of it as well. He has played a huge amount of cricket since he has come into the international arena and we have seen a little bit of push-back from his body with that elbow injury.
"If he is fit and raring to go you want him in your side. But you want to make sure that he is able to deliver all of his skills and not just seam it around and swing it, but do it all at 90 miles an hour."
Wood's chequered past with injuries means the selectors are cautious over him as well, and Root suggested that he, like Archer, must be able to bowl at full pace to get into the line-up.
"The reason we have been quite cautious in terms of rushing him back is that (injury) history and knowing that his value in the team is being at 100%," the skipper added.
"If he is 100% and firing, the skills he has at his pace will be a great asset in test cricket."
One player who will definitely play a prominent role is all-rounder Ben Stokes, who was named ICC Player of the Year on Wednesday.
"It is hard to say any more superlatives, it is the right decision and it could not really have been anyone else," Root said.
"The way he has performed across all the formats has been fantastic. In my opinion he is definitely the leading player in the world at the moment."
The series is level at 1-1 after South Africa won the first test. (Reporting by Nick Said Editing by Christian Radnedge)