Lidl is about to complete development of a new store at Invertiel - it will replace its existing Esplanade shop.
But the company is also looking at potential sites in the north/east of the town.
It has called on landowners with suitable locations to get in touch.
The sites have to be prominent, easily accessible, and have a strong pedestrian or traffic flow.
The developments form part of the discounter’s ambitious plans to have 1,000 stores throughout the UK by the end of 2023.
Ross Millar, Lidl’s regional director for Scotland, said: “There are towns that will be new for Lidl and in some places, the potential to even double our sites.”
Lidl has committed to investing £1.3bn in its store expansion.