In an August 18 judgment released today, the Supreme Court granted leave for appeal to hear whether the Court of Appeal was correct to conclude that Radhi's circumstances did not warrant a reference to the Minister of Justice under the Extradition Act.
The minister has a wider discretionary power under the legislation, not available to the courts, to refuse an Australian extradition request.
Radhi applied to the District Court in February 2015 for an order referring his case to the minister, but the District Court turned him down.
Subsequent appeals to the High Court and Court of Appeal were made but also lost.
Radhi's lawyer Ron Mansfield argued last week that if his client was sent to Australia for more than two years for a trial he would lose his New Zealand residency and be unable to return to his family.
In their judgment, Justices William Young, Ellen France and Mark O'Regan said the District Court evidence about what is likely to happen to Radhi, if he was required to stay in Australia for longer than two years, was "limited".
The justices said if there was no agreement about the likely consequences for Radhi then further evidence could be filed to be considered.
Two other people have already been tried and convicted in Egypt and Australia for the people-smuggling operation.
Radhi was living in Indonesia at the time of the sinking, having arrived there in March 2000.
He was subsequently recognised as a refugee under religious persecution grounds by the United Nations High Commissioner for Refugees and put forward for inclusion in New Zealand's annual quota intake of refugees.
New Zealand granted Radhi refugee status, and he and his wife and two children arrived in New Zealand in March 2009. Upon arrival, he was granted a residence permit.
However, in October 2010, Australian authorities submitted an extradition request
to New Zealand and in 2011 Radhi was arrested.
Legal proceedings have been ongoing since then as he fights the extradition process.
Radhi's third child was born in New Zealand and his family now lives in Auckland.