However, the council has little else to say about the "confidential recruitment process" under way.
Chairwoman Gretchen Robertson confirmed the council was at a "long-list" phase.
"This is a hugely important appointment for the organisation," Cr Robertson said.
"The council is working through a confidential recruitment process and will be happy to notify the public as soon as any new information becomes available."
Applications for the role closed on November 9 and councillors discussed the next steps in the process with Wellington business management consultant RDC group director Doug Craig in a closed-door session last week.
On Monday, councillors will again meet behind closed doors to discuss the next steps.
The council declined to say what was discussed at the November 24 meeting.
It declined to say whether all councillors, or a committee of councillors, will create a short-list of candidates.
It has also declined to to say when a new chief executive was expected to be appointed.
The new chief executive will replace Sarah Gardner, who left the council for a job in Wellington in May, giving only one week’s notice.
After Mrs Gardner’s departure, an investigation by retired High Court Judge Sir Graham Panckhurst into the council’s response to illegal dumping in the Clutha River highlighted communication failures and an absence of transparency at the council.
Staff were communicating with the chief executive, but the chief executive had not communicated vital information to the councillors.
It could not be put down to a mistake, Sir Graham said.
Instead it showed the relationship between the chief executive and the chairman and councillors was "unwell, if not broken".
Since June, the council has been led by interim chief executive Pim Borren.
The council has declined to say whether Dr Borren has applied for the permanent role.
