Trainer Kevin Barry was surprised Team Fury had left it late to dot down in New Zealand ahead of such an important fight, but maintained that there was still plenty of time for Fury to ready himself for what will be his first challenge at a world title.
"Look there's still two weeks out to the fight," Barry said.
"There's plenty of time for them to arrive, we made an offer to them a while back that they could come out here six weeks before the fight.
"Every international team that we've bought out here in the last four years, we've been very, very accomodating to them, we've put them in the best hotels, we've had drivers with them, we've flown them very well and it surprises me that they are leaving it to this late stage to arrive down."
Parker was also critical of Fury's timing of arrival leading up to the fight, especially for a boxer who has never previously dealt with jet-lag, he said.
"He's never done jet-lag before, so for someone who hasn't done it before, they should be down here acclimatising to the time and all sorts of stuff like that," Parker stated.
"I've done it before so I know what it takes to get my body used to it and I know I will be ready so I'm not sure how they'll react to it but lets see what happens."
All 20 of Fury's previous professional fights have taken place in either Europe or the east coast of North America, meaning the bout against Parker will be by far the furthest the Englishman has had to travel for a fight.
Despite the secrecy surrounding his arrival date, Fury can be expected to be in the country within the next few days, as the Stockport-born fighter is scheduled to hold a press conference in Auckland on Wednesday.
