Answering questions at estimates, Mr Barr said former prime minister Malcolm Turnbull approached him personally through messaging app WhatsApp.

"The prime minister WhatsApped me and said 'I want to talk to you about Norfolk Island ahead of some more formal engagement with the Commonwealth'," Mr Barr said.

"As a personal favour to the then prime minister when he contacted me and we spoke I said 'Yes I will look at this'. When the prime minister rings and asks, you would generally want to at least give it a fair hearing."

In a wide-ranging discussion, the Chief Minister said the views of Norfolk Islanders would need to be taken into account when deciding the way forward.

Fairfax Media revealed last month the ACT government had been approached by the federal government about the possibility of delivering some state-based services like health and education to the island, which is about 1400 kilometres off the east coast of Australia in the Pacific ocean.

Since the federal government decided to remove the island's self-government arrangements in 2015, services like health and education have been delivered by the NSW government, with the costs met by the federal government.

With those arrangements set to expire in 2020, the federal government has been exploring other options. Since that request from the former prime minister there had been little progress on the question, the Chief Minister said.

A meeting with the new assistant minister with responsibility for the territories, Sussan Ley, was scheduled for the last federal parliamentary sitting week, but was cancelled due to a busy week.

"I have received correspondence from the self-described council of elders on Norfolk Island, outlining a wide range of concerns in relation to their current arrangements. I must say I have a great deal of sympathy for the position that they have put," Mr Barr said.

"I would indicate that the ACT is not rushing into service provision on Norfolk Island and in fact I would consider it highly unlikely that we would become involved. Nevertheless I will hear out the Commonwealth on this matter."

Asked if there would be any benefit to the ACT if the territory was to deliver the services, the Chief Minister could not think of one.

"I'm struggling to see them at this point in time, but I'm aware there is a challenge and a problem for Norfolk Island," he said.

The Chief Minister said it would be a "necessary prerequisite" for Norfolk Islanders to want the ACT to provide services on the island for any plan to go ahead.

"I think, first and foremost, Norfolk Islanders - we would need their support. I suspect that given the tenor of the correspondence from the council of elders on the island that there are a range of issues that they would wish to work through with the Commonwealth before engaging with us and I think that is appropriate."

He also revealed that he had been invited to visit the island, but wouldn't do so ahead of any further discussions with the federal government.

With elections due both in NSW and at the federal level in the first half of next year, the Chief Minister said it was unlikely anything would be resolved in the current term of federal parliament, but that he remained at the table.