"Our hope is that we may have a travelling exhibition in the first instance, and then have Te Papa be the guardians of the artefacts," Mr Foon said.
Replicas could be made for a museum in Guangzhou, the province where most of the miners came from. The NZCA would make a submission to the ministry, he said.
"It's important that we make our views known and respond appropriately to the wishes of the Chinese descendants of the SS Ventnor."
The removal of objects from the wreck before it came under Heritage NZ protection initially sparked anger from some members of the Chinese community.
But Mr Foon, who is also the Mayor of Gisborne, said the NZCA thanked the divers, led by film-maker John Albert, for bringing the artefacts to the surface and handing them over to the police museum for safekeeping.
"We ask that all parties be respectful to each other and agree to work on this project collaboratively for the betterment of all involved."
Mr Foon said the Chinese community was also grateful to Te Roroa and Te Rarawa iwi, who discovered the miners' remains along the west coast more than 100 years ago and buried them alongside their own people.
Their manaakitanga (hospitality) and kaitiakitanga (guardianship) for ancestors of the Chinese community was "very spiritual and moving", he said.