Mr Cooney has held the position for seven years but said he would not be reapplying for the job at the end of his current term.
He did not have any other plans at this stage but would be staying in Alexandra, he said.
The council has a legal responsibility to advertise the position at the end of the contract.
Mr Cooney was employed on a five-year contract, with the right of renewal for a further two years.
"The council voted to take up that option two years ago without advertising the position at that time, as it was allowed to do," Mayor Malcolm Macpherson said.
"This time we have to advertise, even if Mr Cooney wanted to stay on," he said.
The position is not expected to be filled until well into the new year.
Mr Cooney has said he would be happy to stay on as a consultant after his contract expires in January to help work through and bring to a conclusion the council's Vanguard programme, aimed at improving the way council operates.
The CODC had been a great place to work, the staff were good people to work with and Central Otago had a varied and interesting community, he said.
"I remember one of the questions at my interview for this job was 'how would I get things going here?'
"That was just at the time the property market started to take off, and after seven years I have seen quite significant changes for the community. It was a good time to be involved," he said.
