Noelle Adeley, a resident in Blandford, Dorset, has started a petition calling for Waitrose to take over an empty store in the town vacated by Safeway in April.
She claims the retailer would benefit the area and hopes to collect 2,000 signatures.
However, a spokeswoman for Waitrose said that although it was always interested in new sites, it had no plans for Blandford.
Meanwhile, protests against new store openings are continuing. Residents in Halesworth, Norfolk, have formed the Halesworth Against Second Supermarket Lobby after a local businessman sold a piece of land to property developers Albourne Estates, which has submitted plans for a supermarket on the site.
In Bognor Regis, West Sussex, Tesco has disgruntled businesses by submitting planning permission for two sets of traffic lights outside its store in the town. Traders at a business park opposite the store claim their entrance would be blocked by traffic.
And in Finchley, London, residents and shopkeepers have spoken out against a proposed second Tesco Express in the area. The store is situated near an existing Tesco.