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Proposals for a new store on the former B&Q site at Inglis Green Road have been developed by owner Morbaine Ltd.
The developers said the aim of the design, was to make the best use of the space by providing parking space beneath the shop.
It could give the 80,000 square feet development a valuable edge in competing with the nearby Asda at Chesser.
The designs for the proposed supermarket – which does not yet have an operator – will be shown to the public next week.
Developers said the aim of the "split-level" building was to ensure they could make the best use of what is a restricted space, allowing them to include a large, enclosed car park without reducing the size of the store.
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Alex Brodie, director of Morbaine, said: "This is an exciting project for a number of reasons, not least because it will bring up to 400 new full and part-time jobs to this part of Edinburgh.
"It will also bring some much-needed additional choice for shoppers. Currently, Asda is the only large supermarket serving people in Longstone and the surrounding areas. The extra competition this proposed new store could provide has got to be a good thing.
"The proposed store is on two levels – with a secure, weatherproof car park on the ground level and the retail floor on the upper level linked by special 'travelators'. As such, it would be one of the first of its kind in Scotland."
Several shops with a similar design have opened in London over the last two years, and Scotland already has one such supermarket, in Galashiels.
Although a retailer has not yet been selected, Morbaine said several national supermarkets had expressed interest in the site.
Graham Birse, deputy chief executive of Edinburgh Chamber of Commerce, said: "The proposed development by Morbaine is exactly the kind of investment Edinburgh needs to help us rebound from recession. It's important that we find sustainable economic use for this site in order to create jobs and value for local people.
"Shoppers will benefit from increased choice and the extra competition generated will help ensure they are getting value for money."
A public exhibition outlining the design, which will include artists' impressions of the proposed store and a chance to talk to members of the project team, will be held at Slateford-Longstone Church Hall on Wednesday, 14 April, and Thursday, 15 April from 10am to 9pm both days.