"We would like an opportunity for as many players as possible to be involved in an official celebration if this is possible."
Wellington's mayor has already put his hand up for the capital to host a parade or civic service.
Public affairs advisor Hayden Munro said Mayor Justin Lester made the offer "almost immediately" after the team won.
He said they were still in talks with New Zealand Rugby about the timing and logistics of a celebration.
An Auckland Tourism, Events and Economic Development spokesman said Ateed was waiting on an update from New Zealand Rugby before a decision on any sort of parade could be made.