That list will be provided to the Prime Minister who will then – after consultation with Ministerial colleagues – decide whether or not to accept the list.
After the Solicitor-General confirms the candidates' willingness to be appointed, the Prime Minister will make her recommendation to the Governor-General, after consulting with Dame Sian.
"Given the significance of the role of Chief Justice in New Zealand's constitutional order, it is important that the appointment process is conducted against transparent criteria," Ardern said.
Although the process involves no formal consultation with the Opposition, a Spokesman for the Prime Minister said she is not precluded from talking to Shadow Attorney General Chris Finlayson about the decision.
A Spokeswoman for National said Finlayson was "really comfortable" with the process as it has been laid out and he is confident he will be consulted properly.
The appointment process is expected to be completed by the end of 2018.
If it is not completed by the time the present Chief Justice retires, the Senior Courts Act provides that the most senior available Judge of the Supreme Court is authorised to act as Chief Justice.
Ardern said the appointment is even more significant as this is the first ever appointment of the head of New Zealand's final appellate court.
Dame Sian was appointed in 1999. At that time the Privy Council was at the apex of New Zealand's court structure.
That, however, changed in 2003 when the Supreme Court was formed.
The Supreme Court Act of 2003 brought to an end appeals to the Judicial Committee of the Privy Council from decisions of New Zealand courts.
Dame Sian will retire in March next year.
To qualify for the nation's top legal job, an applicant must be an "outstanding judge and leader", Ardern said.
They would need to have an understanding of the diversity of the communities, an insight into their differing requirements and an appreciation of the impact of law on society.
A Chief Justice would need to have the ability to engage fully and to deal effectively with members of the Executive, Parliament, the media and professional and other bodies.