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.
White, who was linked with the England job before Eddie Jones was appointed in 2015, is head coach of Japanese top-flight side Toyota Verblitz.
He was in the running to replace Robbie Deans as Australia head coach in 2013, but was beaten to the role by Ewen McKenzie.
Australia finished their worst season in 60 years with a 37-18 defeat by England at Twickenham last week, leading to calls from some fans and pundits for 51-year-old Cheika to be replaced.
Scotland director of rugby Scott Johnson, an Australian, has also been linked with the job.