The prime minister’s strongly-worded message came amid rumours British officials could relocate the convicted murderer to Canada, Australia or New Zealand.
Speaking at a press conference on Monday, Ms Ardern said: “I’ve seen reporting; I’m advised that Immigration New Zealand have not received anything official.
“Of course because of his existing convictions he would need an exemption [under the immigration act].
“My advice would be: don’t bother applying.”
Venables and Robert Thompson, both then aged 10, snatched two-year-old James from a shopping centre in Bootle, Merseyside, in February 1993 before torturing and beating him to death on a railway line.
They were granted life-long anonymity worldwide and have been given a number of identities since their release from custody in 2001 at the age of 18.
Thompson is believed to have made a new life for himself but Venables, now 36, landed himself back in prison in 2010 and 2018 after twice being convicted of child pornography offences.
The cost of funding legal battles to keep Venables’ identity secret are reportedly behind plans to relocate him.
Earlier this year, it was revealed that a bid to protect his anonymity cost taxpayers more than £65,000.
James Bulger’s father, Ralph, and uncle lost a legal battle in March to make more information about the killer public.
According to the Daily Star, officials believe shipping Venables abroad could be cheaper than frequently giving him new identities when he is outed by the public in the UK.
However, it is believed taxpayers would also have to foot the bill for his relocation.