The small birds don't fly far across open ground, and would be unlikely to move from Waitahinga to Bushy Park Tarapuruhi on their own.
Pōpōkatea and tītipounamu (rifleman) are at the top of a list of birds that could be moved into the sanctuary, Bushy Park manager Mandy Brooke said.
Efforts to add pōpōkotea were derailed by the Covid-19 restrictions last year.
Brooke is hopeful the transfer might happen after the next summer.
Before that existing pōpōkatea populations will be surveyed, in November, to ensure they can sustain the removal of birds.
The work will be done by translocation consultant Kevin Parker, who managed the move of toutouwai/North Island robin and hihi/stitchbirds to the sanctuary.
Like pōpōkotea, tītipounamu were once common in North Island forests, but numbers declined and populations became more scattered as forests were cleared.
The process to re-introduce them to Bushy Park is further behind that for pōpōkotea, Brooke said.
Tītipounamu are New Zealand's smallest bird, and a species of wren.
It's too soon to talk about what other species could be re-introduced - but the sanctuary is too small for birds like kōkako.
The Bushy Park forest and homestead were both closed to the public during the Covid-19 alert level 3 lockdown, with essential work continued by managers and volunteers.
Under level 2 the forest will be open to the public again, Brooke said, with people expected to maintain 2m distance from those not in their bubble and either wash or sanitise their hands after pushing the buttons at the gates or using the toilets.
The homestead will be closed to all but house guests under level 2, lessee Dale Pullen said.
