Ioane Teitiota was deported from New Zealand in September after overstaying his visa.
Lawyer Michael Kidd says Teitiota, his wife and three New Zealand born children, are struggling to settle and want to look at moving to Timor-Leste.
He says Teitiota, his wife and three New Zealand born children, are living with his brother-in law in Kiribati.
Kidd says the children have been struggling to adapt to life there, and Teitiota's son has been in particularly bad health.
"His immune system is having difficulty coping with the fact that most of the fresh water comes from reservoirs that are invaded by salt and that are contaminated by human waste. I mean, if he was to become seriously ill I don't think it would make the New Zealand government look very good, would it?"
Kidd says he will be laying a complaint with the UN Human Rights Council and hopes to improve the treatment of those affected by climate change.
"There's a lot of awareness, at least in the European Union, that this needs to be looked at very seriously. The New Zealand government seems to be dragging its feet on providing refuge for people being displaced by climate change. The Fiji government has done a lot."
Fiji sold 20 square kilometres of land for Kiribati to cultivate in a measure to heighten food security.
The prime minister Frank Bainimarama also told the Kiribati president his people should not fear being climate change refugees, and Fiji's doors are open.