The retired professional boxer wants to go to the country in order to attend a series of self-help lectures.
Tyson has recently been stunning theatre critics in New York with his one-man show and is hoping to take the concept to the other side of the world in November.
However, officials at the New Zealand Immigration Service have not yet agreed to give him a visa because of his 1992 rape conviction.
His conviction means a problem for the visa as under New Zealand law, anyone convicted of an offence that has a prison sentence of five years or longer will not be granted a visa unless there are special circumstances.
Despite the laws, Tyson hopes that New Zealand officials will allow him into the country.
He told local reporters on Thursday (August 30): "I'm not going to sit here and cower and beg to come to your country. If I can't come, I can't come. It will be my misfortune but I don't want to feel like I'm on trial to come to your country.
"I've never been to New Zealand. I've never had the opportunity before. It must be a serious country if I can't go there."
Tyson's promoter Mark Markson added: "He's a great ambassador and he really does have a tremendous story which he has to tell to the people of New Zealand and it would be a tragedy if the show that he's been doing on Broadway for the last few weeks can't be told."