Mr Dutton has spent years pushing back against a campaign to let the family return home to Biloela.

He has long argued they are not owed protection and should be sent to Sri Lanka.

"It's been a frustrating case because every court, every tribunal, every decision maker has been very clear to this family that they are not refugees," Mr Dutton told Nine Entertainment.

"This family has not ever been found to be owed protection."

The Murugappan family was relocated to Perth after four-year-old Tharnicaa was sent there for medical treatment.

They will be allowed to stay in Perth until their legal fight against deportation is resolved.

But they will not be allowed back to Biloela and the government has not decided whether any of the family members can reapply to stay in Australia.

Mr Dutton claimed showing the family compassion would sent the wrong signal to people smugglers.

"We've got to be very careful," he said.

West Australian Premier Mark McGowan said it was "preposterous" to suggest people smugglers were watching the case.

"This is a family of a meat worker, his wife and two Australian-born kids from a regional town in Queensland," Mr McGowan told reporters.

"They should just let them go back there and live out their lives."

Australian Associated Press