Since the All Blacks' victory over France on Sunday night, the team has paraded the Webb Ellis Cup in Auckland on Monday and in Christchurch yesterday, with Wellington the venue today.
New Zealand Rugby Union spokesman Nick Brown confirmed there were no plans for a parade in Dunedin because the team was disbanding tonight.
However, that has not stopped a rugby-mad family from setting up the Facebook page, "We want a victory parade for the All Blacks in Dunedin", which last night had more than 4000 members.
Organiser Emma Lowe said the decision "felt unfair" as Dunedin, with its new stadium and the welcome it laid on for the thousands of rugby visitors during the rugby tournament, deserved better.
"It seems only fair that the people of Dunedin get the opportunity to offer their congratulations to a team that have really realised an entire nation's dreams."
Dunedin-based MPs Michael Woodhouse, Clare Curran and Metiria Turei and Dunedin Mayor Dave Cull have also lent their support for an All Black celebration in the city.
Mr Woodhouse said while it might not be possible to get all the All Blacks to come to the city before they disbanded, he had spoken to the NZRU, which had suggested a possible trophy tour.
He hoped some of the South Island-based players could join that tour and would work with Ms Curran and Mr Cull to ensure the city could celebrate.
Mr Cull said there had been talk that the city, along with other South Island centres, could look at encouraging "a bit of a tiki tour with all or part of the All Black team, but we have yet to progress that".
Mrs Turei said a parade would be great for the city.
"Even if we can't get all of them, we should get some of the All Blacks," she said.
