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The i-Sites are in Centennial Ave, Alexandra and in The Mall, in Cromwell.
Employees have reportedly been told to justify to the Central Otago District Council how to make the visitor information centres viable in a vastly changed tourism environment, amid restrictions resulting from the Covid-19 pandemic, and its economic ramifications.
The council is not providing information.
Central Otago Mayor Tim Cadogan referred all comment to Central Otago District Council chief executive Sanchia Jacobs.
"She is having discussions with some staff, but as their employer you would have to go to her [Ms Jacobs]."
Ms Jacobs said the council was looking at a range of measures to help reduce the financial impact of Covid-19 on ratepayers across the Central Otago district.
That meant decisions had to be made.
"The economic challenges facing our country, and indeed the globe, are unprecedented and require all parties to act.
"It is inevitable that some of those decisions will be difficult ones when it comes to the operations of council and the services it delivers.
"The community is always at the forefront of those decisions."
She would not be drawn on the future of the Alexandra and Cromwell i-Sites nor staff possibly affected.
"I am sure you can appreciate that as an employer it would be absolutely inappropriate for me to discuss any confidential employment matters with any other person not involved in those matters."