A Tamil asylum seeker family detained at a Christmas Island facility has had no communication with the federal government about the prospect of being sent to the US or New Zealand.
The Murugappan family's lawyer Carina Ford on Wednesday responded to suggestions the two countries were likely destinations, as the government continues to reject pleas they be allowed to remain in Australia.
"For the record we and our clients have not been approached about this by the Government - we have written to the Department of Home Affairs to ask why," Ms Ford tweeted.
The family has been on the island, far off the West Australian coast, for two years after being removed by federal authorities from their home in Biloela, Queensland.
The Home Affairs Department had been threatening to send them back to Sri Lanka, despite the family's pleas they would be targeted.
On Tuesday, Home Affairs Minister Karen Andrews said "a range of resettlement options" were under negotiation.
Foreign Minister Marise Payne later expanded on that statement, saying the US and NZ were options.
"I do know that the Minister for Home Affairs, Ms Andrews, has indicated that there are two options there and the United States and New Zealand are both in the frame," she told Sydney radio 2GB.
The family has an ongoing court proceeding related to their case, which would normally preclude any sudden change in their resettlement status.
Supporters of the family will hold candlelight vigils in Perth - where the youngest daughter is battling a blood infection - and Sydney on Wednesday.
Three-year-old Tharnicaa is being treated at the city's Children's Hospital after being evacuated from the island with her mother Priya Murugappan earlier this week.
The potentially deadly blood infection has been linked by supporters to untreated pneumonia.
"We've had two delays in treatment here, which has led to this crisis point," family supporter Angela Fredericks said on Tuesday.
Priya says her daughter was sick for almost two weeks and medical contractors at the immigration detention centre repeatedly refused to take her to hospital.
"I want to thank everybody for their love and good wishes," Priya said in a video message as she cradled her daughter.
"I hope that Tharnicaa can get the help she needs now. Please, help us to get her out of detention and home to Biloela."
Contractor IHMS said in a statement to AAP on Wednesday the child had received "appropriate and timely medical care".
"Due to privacy reasons we are unable to respond to specific questions relating to the medical treatment and condition of the individual.
"IHMS and its employees take the health and welfare of all our clients very seriously and work tirelessly to support all those in our care."
Home Affairs and Australian Border Force said Tharnicaa had been receiving medical treatment and daily monitoring on Christmas Island consistent with medical advice.
"As soon as the ABF was advised by the treating medical practitioners that the minor required medical treatment in Western Australia, the minor was transferred to a hospital in Western Australia," an official said.
"The Australian Border Force strongly denies any allegations of inaction or mistreatment of individuals in its care."
Healthcare for detainees was "broadly comparable" with that on the mainland, the government has said.
Priya, her husband Nades and their Australian-born daughters Tharnicaa and Kopika, 6, have been in detention since 2018, and on Christmas Island since August 2019.
The government has previously vowed to never permanently resettle anyone who arrives illegally by boat.
The vigils will be held outside the hospital on Wednesday evening and at Sydney Town Hall on Thursday.
