Peter Fury, the father and trainer of heavyweight boxer Hughie, Joseph Parker's opponent in Auckland in May, has lodged his visa application with New Zealand Immigration and is confident he will be allowed entry despite his criminal record.

In 1995, Englishman Peter Fury, now a key part of Hughie's camp, was jailed 10 years for drugs possession and intent to supply. In 2008, he got another two years for drug-related money laundering.

New Zealand's immigration rules require a special exemption and character waiver for those wishing to enter the country, who have served more than five years in prison.

Parker's promoter David Higgins said recently he hoped Peter would be given an entry visa to support his son, but wouldn't comment publicly about whether he would officially support it.

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In an interview with IFL TV, published this morning, Peter said the paperwork had been lodged.

"The slightly disappointing thing is we have to go through the visa issues again, but what can we do? The visa now has been lodged, we've put it in, so we're optimistic.

"It's a Commonwealth country. I've been to Canada, that's a Commonwealth country - I had no problems there, so I'm optimistic it will be okay."

Asked whether he expected to travel for the fight, Parker's first mandatory defence of his WBO title, at Vector Arena on May 6, he said: "It's down to New Zealand immigration, I can't say.

"Whatever their decision is, I'll respect it. They've got a lot of paperwork.

"I've covered every detail, all my past record ... when, what, if. It's taken about three weeks to get it all together."

Section 15 of the New Zealand Immigration act reads: "In accordance with immigration instructions, certain criminal convictions will mean that the person is normally ineligible for the grant of visa unless a character waiver is granted.

"When considering a character waiver, each application is considered on its individual merits and taking into account factors such as the seriousness of an offence, number of offences and how long ago the event/s occurred."

Asked how impressed he was with 25-year-old Parker, undefeated after 22 professional fights, Peter Fury said: "I am impressed, I don't change my view, because he's fighting world-class opposition.

"[Andy] Ruiz was a good fighter, a very good fighter. [Parker has] fast hands, he can punch, [and is] a good combination puncher.

"And [the Carlos] Takam [result] speaks for itself - they're world-level operators aren't they? You're never going to have an easy night with these guys."

Peter, the uncle and trainer of Tyson Fury, said it was unlikely the former world champion heavyweight would return to the ring in May, as announced on social media.

"He wouldn't be far off, but there are issues to deal with first," Peter said. "Nothing is firmed up and I see it as unlikely."

Tyson, who has had mental health issues and admitted to a cocaine addiction, is still suspended by the British Boxing Board of Control and his licence is not close to being reinstated.