Nauru Airlines planes have been seen at Adelaide airport, and advocates say they are aware of four or more families that had arrived in the past fortnight.
Asylum-seeker families are being quietly flown from Australia's offshore processing centre on Nauru to Adelaide, according to some advocates.
Nauru Airlines does not fly commercially to Adelaide, but its planes have been seen at the airport as recently as Monday.
The latest monthly figures from Border Force are for the month from September 1 to September 30, when there were no asylum seekers transferred to Australia or any other country.
But some families have been moved more recently, according to advocates on the ground who work with asylum seekers.
Activate Church pastor Brad Chilcott told SBS News he was aware of between four and seven families that had arrived in Adelaide from Nauru over the past four weeks. They were all families that included young children who needed urgent medical care and were now receiving it at Adelaide's Women's and Children's Hospital, he said.
Mr Chilcott has not been in direct contact with the families since they arrived, but has worked with previous medical transfer cases in Adelaide. Until now, most medical transfers were triggered by Federal Court orders, despite attempts from the Home Affairs department to prevent them.
He said the government was still insisting all the families would be returned to Nauru once they were medically fit - but predicted doctors would be reluctant to sign off on returning patients to the Pacific island nation.
The asylum seeker advocate said there were "political realities" forcing the government to proactively move the families. The election of independent Kerryn Phelps in Wentworth raised the prospect of a Labor, Greens and crossbench revolt to bring all children from offshore detention centres to Australia.
Earlier in the week, prime minister Scott Morrison said the number of children on Nauru had halved in nine weeks. "We've been getting about this quietly, we haven't been show-boating about it," he said.
SBS News has contacted the Department of Home Affairs for more information, including on whether the families are only in Australia for temporary medical treatment.
A spokesperson responded to the series of questions with a single line:
"The Department does not provide specific details on the transfer arrangements of individuals."
Defence minister Christopher Pyne, the government's most senior South Australian, said he was not aware of the specific details.
"I don't know if that's to Adelaide, I haven't made those inquiries, I've only seen that story myself this morning, but if that's the case I think most people would welcome that outcome," he told 5AA radio on Wednesday.
The government has been under pressure from Labor, the Greens and some members of the crossbench to transfer the roughly 50 remaining children and their families from Nauru to Australia for medical assessment.
The push is also supported by the Australian Medical Association.