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In February, Mr Ross said he would leave the post he had held since January 2004 in June, six months ahead of schedule.
The Otago Daily Times reported last month 72 applications were received for the role and at last week's council meeting, Waitaki Mayor Gary Kircher said the shortlist was down to five candidates.
''We've got some really good choices - some diverse choices,'' he said.
''It's an exciting time.''
He said the executive committee - Mr Kircher and Crs Craig Dawson, Peter Garvan, Melanie Tavendale and Colin Wollstein - would begin interviews ''in a couple of weeks''.
Mr Kircher told councillors he would try to have ''all of us as involved as possible'' through the process.
The mayor's report to council on May 10 stated the two top candidates as chosen by the executive committee would then undergo a ''comprehensive interview'' by the full council.
An appointment was expected in June.
''It's quite a long process, but one which we expect will give us a great [chief executive] to lead the operational part of this organisation into the future. This is probably the single most important decision this council will make in the whole term,'' Mr Kircher's report said.
When he announced his intention to leave the council earlier than planned, Mr Ross said bringing in a new chief executive at this stage would complement the long-term plan budgeting process for the next three years.
He said he would ''like to try and get closure on ... the Alps 2 Ocean Cycle Trail, the Oamaru Courthouse, and the direction for the former RSA building project'' before he left.
Mr Kircher said the council was focused on improving customer service and communication when the search to replace Mr Ross began.
The council's recruitment consultant called the 72 applications the council received for its chief executive position ''unusually high''.