The Sydney Morning Herald reported the plans were for a four-week tournament this year.
The centrepiece of the proposed tournament would be a double-header at Auckland's Eden Park in which Samoa and Tonga would meet in a repeat of their World Cup quarter-final, before Australia and New Zealand do battle.
It would also see Australia and Samoa repeat their World Cup final of October 2022, won by Australia.
The Herald says the emergence of Samoa and Tonga has made a competition in the southern hemisphere a potential money spinner, in particular if the Pacific powerhouses meet in Auckland, which has a large expat population.
A competition would be seen as a crucial platform for the next World Cup, which will be held in 2025.