The group salvaged a number of objects they planned to send to a museum in the miners' home province in China.
The objects are a brass porthole, a bell, a plate, a lamp holder and part of a ship's telegraph machine.
Groups representing the miners' descendants were upset at the prospect of the relics going overseas, however. They also viewed the wreck as a mass grave that should not be interfered with.
At their urging the Historic Places Trust - now Heritage NZ - rushed through legal protection for the wreck, which is now a protected archaeological site with stiff penalties for anyone removing artifacts.
The Ventnor objects were removed from the wreck before the protection came into force, but were handed over to police for safekeeping and stored at the Police Museum in Porirua until ownership could be determined.
A notice from the Ministry of Culture and Heritage in various Friday newspapers, including the Advocate, invites parties with interest in the objects to either provide proof of ownership or make submissions about the objects' future care. The closing date is November 23.
A spokeswoman said if the objects were not claimed the ministry would decide where they should go after consulting all interested parties and reviewing the submissions.
The Ventnor Group, which represents descendants of the Chinese miners, was not able to respond by edition time.
Any pre-1900 archaeological sites are automatically protected by law. The Ventnor sank in 1902.