Rugby Australia said it was approached by White, who led the Springboks to World Cup victory in 2007.
Wallabies boss Michael Cheika's future is in doubt after his side lost nine of 13 Tests this year.
White was due to talk to Rugby Australia chief executive Raelene Castle yesterday.
The governing body confirmed the South African had initiated a "conversation" with Castle, and a phone call between the pair had been arranged.
"The call as reported will not be going ahead," Rugby Australia said.