Pienaar made his debut against New Zealand on Saturday at full-back - the position his father Gysie played in the 1980s for South Africa.
And White claims the team dynamic dictates Pienaar has to continue playing at number 15 for his country.
"People ask me about Ruan and I say where do you play him? If you drop a guy like Fourie (du Preez), who has almost 30 Test caps, and start again with a young scrum-half, you have to believe that in 10 Tests' time that he will be better than Fourie will be with 50 Tests under his belt," White said.
"Fourie didn't play badly so then you weigh up where else you can play him (Pienaar). Can you play him at fly-half?
"If you're not convinced he is a fly-half, then you've got to find a position for him.
"There is no doubt that anyone who watches rugby knows he can play. We've got to find a place for him.
"If he is going to be part of this squad going forward, then the one area where he can add value is full-back.
"He kicks well, counter-attacks well and understands how to use space. That is one area that we're looking at," White added.
Pienaar may be an option this week when the Boks face the All Blacks again.
The New Zealanders won 45-26 at Loftus Versfeld to give their coaching staff their first victory in South Africa in three years.
The Bok management gave the entire squad the day off on Monday as they continued to lick their wounds from the defeat.