Prime Minister Jacinda Ardern has a sharp message for British child killer Jon Venables and the possibility of him relocating to New Zealand: "Don't bother."

British media have reported that Jon Venables, the co-murderer of 2-year-old James Bulger, could be shipped from the United Kingdom to New Zealand to start a new life.

Venables was granted lifelong anonymity after he was found guilty of murder when he was 10.

The cost of funding fund legal battles to keep his name secret is reportedly behind the relocation plans, with Canada the most likely destination, but New Zealand and Australia as possibilities.

Asked about this at her post-Cabinet press conference today, Ardern had a stern reply.

"I'm advised that Immigration NZ have not received anything official. Because of his existing convictions, he would need an exemption under [the Immigration Act].

"My advice would be: 'Don't bother applying.'"

New Zealand immigration law permanently bars entry to anyone who has been sentenced to a jail term of five years or more, but the Immigration Minister has discretion to grant a visa in special cases.

Immigration NZ spokeswoman Yvette McKinley told the Herald the agency had not been approached by UK authorities regarding Venables.

Bulger died after he was snatched by Venables and Robert Thompson, also aged 10, from his mother in a Liverpool shopping centre in 1993.

The pair tortured and killed Bulger, and tied his body to a train track in Merseyside, Northwest England.

Both killers were granted lifelong UK taxpayer-funded anonymity and given new identities when they were released from life sentences in 2001.

Venables, now 36, has been convicted twice since his release, once in 2010 and again in February 2018 after admitting to possessing "sickening" child porn images and a paedophile manual.

Earlier this year it was revealed it had cost the UK taxpayers £65,000 ($125,642) in legal battles to keep his identity a secret.

In March the father of Bulger, Ralph Bulger, wanted to identify Venables publicly after he was jailed for possessing child abuse images.

In his legal battle, Ralph argued information about Venables which was already "common knowledge" should be made public, adding that certain details about him were easily accessible online.

However, the UK's president of the family division, Sir Andrew McFarlane, refused to change the terms of the order, saying it was a "wholly exceptional case" which was designed to protect the "uniquely notorious" Venables from "being put to death".

According to The Guardian, he said: "There is a strong possibility, if not a probability, that if his identity were known he would be pursued resulting in grave and possibly fatal consequences …My decision is in no way a reflection on the applicants themselves, for whom there is a profoundest sympathy. The reality is that the case for varying the injunction has simply not been made."

Bulger's mother Denise Fergus told the BBC at the time she didn't support the legal bid, saying she does not want "blood on her hands".