The exiled father of AFL star Dustin Martin failed in his bid to return to Australia last weekend, following a landmark High Court ruling that indigenous people could not be deported.

Mr Martin says he has an Aboriginal grandmother from Tasmania.

The Age also reported on Tuesday that Mr Martin and his three sons, including Dustin, were issued certificates confirming their Aboriginality by the Aboriginal Corporation of Tasmania in December 2016.

But that organisation was deregistered two years ago, according to the Australian office of the registrar of indigenous corporations.

Heather Sculthorpe, chief executive of community service organisation Tasmanian Aboriginal Centre, says there is no way they would say Martin has Aboriginal heritage.

"We would never have certified Shane Martin to be aboriginal, we have never seen any evidence that he is aboriginal," she said.

"No one in Tasmania has ever heard of him to be aboriginal."

Martin was deported to New Zealand after living in Australia for 20 years because of his links to the Rebels bikie club.

Home Affairs Minister Peter Dutton slammed the door shut on Martin after his failed bid to return to Australia last weekend after claiming he had Aboriginal heritage.

"Part of the reason that we kick out people with severe criminal histories, like Mr Martin, is that we want to make sure that people don't commit crimes again in our country," Mr Dutton told the Nine Network on Tuesday.

"I think he's got a spurious claim but that is a claim for him to put," he said.

Mr Dutton is confident the court decision won't create an avenue for the father of Richmond's Brownlow medallist to return.

"We have now cancelled the visas of about 5000 people, many of them involved in outlaw motorcycle gangs, who are the biggest distributors of amphetamines, ice in our country, destroying lives," the minister said.

"It's a very clear message that if you come to our country as a Kiwi, a US citizen, as citizen of anywhere else in the world and you commit crimes in our country, you can expect to be deported."

Mr Martin was put on the first flight back to Auckland on Monday after having arrived in Sydney with a lawyer on Sunday.

Australian Associated Press