1982 All Whites captain Steve Sumner says the 2010 All Whites deserve nothing less than a ticker-tape parade when they return from South Africa.
New Zealand is out of the World Cup there after recording three points in three matches in Group F. The All Whites were not beaten.
But an official celebration could be up to a month away as players and coaches return home at different times or go to their homes overseas.
Football New Zealand says it will not be simple to organise a celebration because of the logistics.
Sumner acknowledges a ticker-tape parade may not happen. But he urges people to welcome the All Whites home when the first of the players arrive at Auckland international airport on Sunday afternoon.
Wellington City Council has indicated a friendly match between the Phoenix and the Argentinian club Boca Juniors on 23 July might be the day to celebrate.