The position is being performed by Clare Hadley, who was appointed to the role in March 2018, but her five-year contract will expire on March 8.
The council could have offered Mrs Hadley the position without going on the market, but it has decided to carry on with a recruitment process.
Invercargill Mayor Nobby Clark said short-listed candidates would be interviewed early next week and a formal announcement around the position would be made on Tuesday.
He was optimistic about the future of the council and the amount of applications as he believed the council had managed to improve its reputation, resulting in a good pool of candidates.
"Council and staff are working well at the moment, which includes the chief executive — no issues here for me," he said.
"We’ve employed an external recruitment organisation and they advertise both nationally and internationally for people that might be interested in coming to this type of job. It is quite a high-level job with an attractive pay range."
Mr Clark said it was not appropriate to comment on the salary for the position but public documents showed Mrs Hadley’s annual salary was about $365,000.
Of the 33 applications received by the council — 75% of those came from professionals from outside the region, he said.
Four of them were shortlisted but one had withdrawn their application.
"I was surprised to get that many. Some of them were strong candidates but I think some of them just saw an opportunity in Invercargill and tried to throw their name in the hat.
"We’ve got a solid group of three people that we want to interview — which is great."
Mr Clark refused to confirm if Mrs Hadley was among the candidates, saying he did not think it was appropriate to comment on particular names.
Mr Clark said the council’s external consultant had already spoken to the shortlisted candidates and arranged psychometric testing and referee checks — the trio would be interviewed on Monday.
"Two elected members will run the interviews and the other 11, which includes me, will sit on the side and just observe."
Mr Clark declined to say who would be asking most of the questions.
"They might not be who most people think it might be but I chose them because I think they have a nice ability to interview somebody. They have the ability to ask impromptu questions."
At the end of this interview, the other elected member would be able to ask some questions.
"I am not going to put a person in front of 13 interviewers," he said.
"That is a mess and that is what happened last time."
All 13 elected members would have a single vote and the successful candidate must have majority support or more than seven votes.
