Tuatara once lived on some of the 200 islands in the strait, but had not been seen there since about the 1870s, Mr Hazley, from Southland Museum and Art Gallery, said.
Negotiations are under way for up to 50 museum-bred tuatara to be translocated to one island under the guardianship of a Southland Maori runanga. For security reasons, Mr Hazley did not want to name the island.
Tuatara are extinct on mainland New Zealand, except in sanctuaries or institutions. In the wild, they live on about 35 predator-free islands.
The reptiles have been reproducing well at the museum since 2006 when the ''tuatarium'' received a new roof to let in UV light essential to their wellbeing and breeding success.
Numbers were now up to about 90, which Mr Hazley said was ''50 to 60 too many''.
Among his charges are Henry, who was fully grown when he arrived at the museum 39 years ago and is believed to be 115 to 120 years old, and his long-term partners Mildred, Juliette and Lucy.
Mr Hazley, who has been looking after the tuatara for 42 years said it had been his life-time ambition to see them re-established in the wild in the South.
The plan was to transfer juveniles up to the age of 6. It was hoped they would breed, although that could not be guaranteed.
Most of the tuatara at the museum have been bred from adults originally from Takapourewa (Stephens Island) in the Marlborough Sounds.
Ngati Koata iwi are the guardians of the Takapourewa tuatara.
Ngati Koata Trust cultural manager Louisa Paul said while the final decision on relocating museum tuatara had not yet been made, the process was under way.
Tuatara originally from Takapourewa have been translocated before, she said.
In 2012, more than 250 were moved to five sanctuaries - four in the North Island and the Orokonui Ecosanctuary north of Dunedin, where there are 89 tuatara, including two on public display.
The museum breeding programme was so successful, new homes were needed, or the programme would have to be stopped or fertile eggs destroyed.
''I haven't spent 42 years trying to save a species just to euthanase animals,'' Mr Hazley said.
Such has been the breeding success, he is appealing for donations of food for his tuatara.
Opportunistic carnivores, they eat small invertebrates, such as lizards, earthworms, beetles, grasshoppers, centipedes and flies.
