Parker, the World Boxing Organisation champion, makes his maiden defence against Fury at Auckland's Vector Arena.
NZ Herald reports Joshua, the International Boxing Federation titleholder, and Klitschko, the former IBF, WBO and World Boxing Association champion, fight for the vacant WBA belt at London's Wembley Stadium.
A total of 90,000 tickets are understood to have been sold for the latter fight alongside an expected million pay-per-view passes, courtesy of an exclusive deal with BSkyB. Budgets suggest the fight will generate more than 50 million in revenue.