White has been on record saying the reason Watson isn't part of the team is that "we have better flankers at the moment".
Watson fired his own salvo with a series of interviews where he said there was bad blood between him and White.
Krige waded into the debate on Wednesday, saying the Springboks were far from the polished outfit they claim to be.
"Just because the Springboks have won their last two Test matches does not mean our problems have been solved," Krige told Die Burger Oos Kaap.
"I believe one must have an open-side flanker in your team and I think Watson is the right man for this position (for the Springboks)."
"He has a major influence on just about every match he plays in. At this stage, he also seems to be a good leader, but we'll have to see how he handles greater pressure as captain."
Krige added Watson was in a class of his own as openside flanker in South Africa.
"We have incredible talent among the loose forwards, but we need more open-side flankers.
"Roland Bernard of the Lions is starting to play well again. I rate him rather highly.
"But, every union must develop and hone open-side flankers if we don't want to come short against other international teams."
Krige has also been impressed by 20-year-old star Pierre Spies, who was man of the match in the 21-20 win over the All Blacks in Rustenburg.
"He is big, strong and fast and looks a fantastic player, but I feel he should be used as a ball carrier because that is his natural game," he said.
"The same goes for Joe van Niekerk. One should not try to turn him into a fetcher if he is a ball carrier."