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The 42 staff at the store have been given until Friday to provide feedback on the proposal. First Union is supporting its members with their response.
If the company goes ahead with the plan, it could shut its doors to the public as early as next month.
The company did not say how many staff at the Maclaggan St store would be affected in that situation.
None of its other stores in Otago or Southland is being proposed for closure.
In a separate move, The Warehouse is asking all of its staff across 92 stores to tell it what hours they can do as the company looks to bring in new rosters.
The Warehouse chief executive Pejman Okhovat said the proposed rosters could lead to the loss of 750 jobs across the country (320 full-time equivalent roles or between 500 and 750 if part-time, fixed-term and casual roles are included).
It is not clear if those job cuts are in addition to the hundreds announced as part of a consultation to close several stores, including Noel Leeming and Warehouse Stationery sites.
The company shut all its stores yesterday morning to talk to staff.
First Union general secretary Dennis Maga said the company told staff at the meetings it planned to eliminate 782 roles, and an additional 137 jobs in store closures.
Mr Maga said he would be appealing to Warehouse bosses later today to retain staff facing redundancy and redeploy them to jobs within the wider group.
"We are clearly disappointed," Mr Maga said.
"What we are saying to the company is give us a chance for these workers to be redeployed."
When it announced its proposal to shut some of its stores and move to an "Agile" operating model in June, The Warehouse said 700 to 950 roles (410 FTEs) could be affected.
That was in addition to a proposal to cut head office staff by up to 130 positions.
The Warehouse in central Dunedin was on the list of stores considered for closure but it appears that has now changed to it becoming an online-only store.
A local retail industry source said The Warehouse was likely to renew its lease at the 35 Maclaggan St site to keep rival store Kmart away from it.
"It is solely designed to keep Kmart out of the market," the source said.
"They know Kmart are interested ... they’ve got right of renewal and they’re going to exercise it."
Mr Okhovat said staff would be able to put their availability or volunteer for redundancy on an app.
The company would then work out if new rosters could be filled.
"If, however, through this process a store does not meet the requirements, we will need to consult further with these team members," Mr Okhovat said.
The company said the way it operated its stores had stayed the same for years, despite changes in the way customers behaved.
It said more than 23% of customers shopped online in the past three years and they were also now "shopping at different times of the day and weekends".
"We need to ensure good roster coverage across all times of day and every day the stores are open," Mr Okhovat said.
"To effectively set ourselves up for future success and to ensure our customers get the best from us, we need to manage our store hours and rosters so that our team members and our customers benefit.
"To achieve this, we are asking our The Warehouse store team members to help us by reviewing some proposed revised rosters."
The company said there would not be any reduction in wages for team members.