The biggest doubt is winger Sean Lamont, who took a blow below the knee, while full-back Hugo Southwell hurt his shoulder in a try-saving tackle in the 36-16 defeat by the Springboks last weekend.
In addition, forward Donnie Macfadyen has a painful chest-bone, with back-row partner White also complaining about a knee problem.
Scotland head coach Frank Hadden could not disguise his concern, but insists he has not reached the stage of calling for re-inforcements.
He said: "We are hoping an extra 24 hours will give us a clearer picture and a lot will depend on whether these guys can run on Tuesday."
Hadden has, however, opted to keep John Beattie in South Africa instead of sending him back to France to link up with the Under-21 side competing in the World Championships.
The Scotland boss said: "Under-21 manager John Jeffrey is comfortable with that and understands how important the situation is for us.
"The bonus is what a good development opportunity it is for John when you consider he is a player who may well have a shot at the World Cup next year.
"This is a good place for him to be and I think everybody is aware of the bigger picture."
Meanwhile, winger Simon Webster believes Scotland can learn from the defeat in Durban when they arrive at the EPRFU Stadium in Port Elizabeth this weekend.
The Edinburgh Gunners man, 25, scored the Scots' only try in Durban and is convinced the team can take heart from the way they refused to buckle under the pressure of the South Africans.
Webster said: "It is always a good feeling to score in a Test, but the game was well over by then.
"But at least it showed us what can be achieved when we do the right things with the ball.
"And we are looking forward to doing more of the same in the return match on Saturday."