Daniel Love, 39, was born in PNG but has lived in Australia since he was five. He has a PNG mother and Aboriginal Australian father.
He does not have Australian citizenship and had his visa cancelled last month after serving a jail term.
Immigration officials say they cannot comment publicly on the case.
Lawyers for Love argue that he cannot be expelled from Australia because he is an indigenous man whose father is an Australian citizen.
“Because Daniel is a member of the Aboriginal race and he is a member of the Australian community, he should not be penalised by laws regarding naturalisation and aliens,” law firm Maurice Blackburn said in a statement to the BBC.
Love, the father of five Australian children, has been in an immigration detention facility since his permanent residency visa was cancelled.
According his legal team, Australian authorities cancelled Love’s visa due to his recent 12-month jail sentence and “substantial criminal record”.
‘Lineage here for generations’
Love has launched a case in the High Court of Australia, pointing out that he is also recognised as indigenous by his community, the Murri people.
His sister, Violet Love, an Australian citizen, acknowledged her brother’s criminal history but said he deserved the same rights as Australian nationals.
“[He] probably has more of a sense of his identity being indigenous, being a Murri man, than he has of his PNG heritage,” she told the Australian Broadcasting Corporation.
“Do you need a piece of paper to have the right to remain here after your lineage has been here for generations?”
She added that her brother did not have any connections in PNG, and did not speak the local language.
Love’s family has lobbied Home Affairs Minister Peter Dutton to use his ministerial discretion to reinstate his visa.
A spokesman for the Department of Home Affairs told the BBC. “As this matter is before the courts it would be inappropriate to comment.”
Visa cancellations on rise
The number of visa cancellations in Australia has increased significantly in recent years, according to government statistics.
Since 2014, laws have allowed visas to be revoked if a person has been convicted of a crime carrying a jail sentence of a year or longer.
In recent weeks, Mr Dutton has faced controversy over his intervention in visa cases involving European au pairs.