There are about 90 people employed at the Meridian Mall outlet.
H&J Smith chief executive John Green said yesterday afternoon an announcement was "imminent".
The Armoury Store in Dunedin is also likely to close.
The company is still hoping to sell its Mosgiel store, for which it has had several expressions of interest.
Mr Green said he was hopeful for a "positive outcome" for staff and the public.
The prominent chain of department stores in the South announced a proposal in May to reduce its network of shops and consolidate its operations back to its home base of Invercargill in order to secure the future of its retail division.
Elsewhere in the South, H&J Smith’s Te Anau and Balclutha shops will still close at the end of July.
The Gore shop is to be downsized at the end of August and the Outdoor World in Queenstown will also close then.
Mr Green said the Queenstown H&J Smith would continue trading unaffected, as would the Armoury Store there.
The closure of the Dunedin H&J Smith will be another blow for the Meridian Mall, where another large retailer, Kmart, has not reopened since it closed in the Covid-19 Alert Level 4 lockdown.
It says it will not open its store until upgrades are done on the building and its seismic strengthening is at a level the company feels is safe.
