James Bulger's killer Jon Venables hasn't applied to move to Australia

Notorious UK child killer Jon Venables has not applied to move to Australia, Peter Dutton's office has confirmed.

The British tabloid, the Daily Star, this week reported that British authorities were considering deporting Venables, 36, who murdered two-year-old James Bulger when he was just 10 years old.

Canada was top of the list, but Australia and New Zealand were also being considered, the story said.

But a spokesperson for Home Affairs Minister Peter Dutton said he had not received a visa application.

"He has no active visa application before the department," the spokesperson told 9News.

When asked if a future visa application would be considered, the spokesperson said they would not comment on a hypothetical.

New Zealand Prime Minister Jacinda Ardern was firmer in her refusal.

"My advice would be, don't bother applying," she said yesterday.

Because of the crimes committed by Venables, he would be considered "inadmissible" under Canada's immigration law as well.

Venables and his friend Robert Thompson kidnapped, tortured and murdered James Bulger in Liverpool in 1993.

His current identity has been suppressed, but he has been jailed twice on child pornography offences since his initial release from prison.

UK taxpayers would foot the bill for Venables' move.