The federal government has been weighing up what to do with the Murugappan family as it faces mounting pressure to let them stay in Australia.

The family's plight is back in the spotlight after four-year-old Tharnicaa was flown from Christmas Island to the mainland for medical treatment.

Tharnicaa's mother Priya is with her at Perth Children's Hospital but her father Nades and sister Kopika, 6, are still on Christmas Island.

It is understood Immigration Minister Alex Hawke will announce their release from detention in Canberra on Tuesday.

However, it is unclear whether he will announce their new visa status or just a process for them to follow in order to get a visa.

A spokesman for the minister said the decision was "imminent".

The release would enable the family to reunite in Perth.

Late on Monday, the Home to Bilo group said Nades had been instructed by the Australian Border Force that he would "get some news tomorrow".

It said there had been no communication with the family's lawyer, Carina Ford.

"Priya & Nades have never given up," the group posted on Twitter.

"Tomorrow, we all hope the Minister does what he's always had the power to do. Bring this family #HomeToBilo."

Deputy Prime Minister Michael McCormack earlier said work was underway to bring Nades and Kopika to Perth.

"I understand the health authorities in WA also make these considerations as to whether the whole family gets reunited," he told reporters.

"But as I understand, there was work being done towards that."

The head of the Western Australian health department wrote to the Department of Home Affairs last week advising the Murugappan family be reunited in Perth.

It was not a plea for compassion but based on clinical advice of the Tharnicaa's treating doctors that she must be with family.

Her treatment for pneumonia and sepsis, a life-threatening blood infection, could take up to eight weeks.

Prime Minister Scott Morrison said the government was considering its options and would take advice from medical experts at the Department of Home Affairs.

Pressure has been mounting on Mr Morrison to let the family stay in Australia, with politicians from across the spectrum calling for them to be allowed to return to their adopted home of Biloela in Queensland.

He has signalled the government could finally back away from its hardline stance and allow the family to stay in Australia, at least on a temporary basis.

"There are options that are being considered that are consistent with both health advice and the humanitarian need and the government's policy," Mr Morrison said.

However, the prime minister said permanent resettlement was out of the question.

"That wouldn't be government policy for a pathway to permanent settlement - that is not the government's policy."

Nine health organisations representing tens of thousands of medical professionals across Australia have signed an open letter calling for the family's release.

Paediatrician Jacqueline Small from the Royal Australasian College of Physicians said the children must be allowed to develop and grow in the community.

"We feel very strongly keeping these children in held detention, particularly offshore detention, represents an extreme and unacceptable risk to the children's health, development and mental wellbeing," she told ABC radio.

"Given both children were in held detention from their toddlerhood, the risks are even higher."

Nationals MP Barnaby Joyce has supported calls for the family to stay in Australia for more than two years.

"Tharnicaa and Kopika were born in Australia," he told Network Seven.

"Now, maybe if their names were Jane and Sally and they were playing in their local netball side, we'd think twice about sending them back to another country which they're not from."

Labor leader Anthony Albanese rejected the argument that showing the family compassion and exercising discretion would somehow restart the people-smuggling trade.

"This is about a family who are here, this is not a threat to our national sovereignty," he said.

Australian Associated Press