The group is made up of three councillors, a member of the Independent Maori Statutory Board and two members of the Friends of Fukuoka Gardens.
Auckland established a sister-city relationship with Fukuoka in 1986 and the garden was built three years later. It was designed and built by volunteers who travelled from Fukuoka.
The Japanese Society of Auckland was upset by the removal of the garden, which immediate past president Masa Sekikawa said was a cultural landmark.
Mr Sekikawa said the community had identified three possible locations - the Domain, the Botanic Gardens and a site within the zoo.
Mayor Len Brown formally apologised for the garden's removal at Japan Day celebrations in February.
His pledge was welcomed by Stephanie Hay, head gardener at the zoo in 1989, who said it was time to rebuild the garden and rebuild the city's relationship with the Japanese community.