Captain Victor Matfield heads the list of doubtful starters after he suffered a groin injury during the 27-15 loss to Australia in Durban last weekend.
Hooker Bismarck du Plessis (knee) is also undergoing treatment while star winger Bryan Habana, who missed the game against the Wallabies with a hamstring strain, will be assessed later in the week.
"Victor Matfield injured his groin when he landed awkwardly after he was pulled down in a lineout," a statement from the South Africa Rugby Union read.
"He sustained a mild strain of his groin and will be assessed again later in the week to determine his readiness to play.
"Bismarck du Plessis injured his right knee during the same match.
"He had a scan and saw a specialist this morning to further determine the extent of the injury. He is doubtful and a decision on his availability for selection will be made later this week.
"A decision regarding Bryan Habana's fitness for this weekend will be made later in the week."
Van der Linde's participation in Saturday's game at Coca-Cola Park looks unlikely after he appeared before SANZAR judicial officer Nick Davidson QC on Monday after being cited for an alleged headbutt.
After a lengthy hearing in Durban, Davidson decided to consider his decision overnight with an announcement expected later on Tuesday.