The chef behind the Six by Nico chain is interested in the former Fopp building in the West End.
Nico Simeone's company has submitted plans for a restaurant, bar and roof-top space at 358 - 360 Byres Road.
The building is currently let out to the Santa Lucia restaurant and Glasgow charity Refuweegee.
Planning papers say the proposal is to link all parts of the building to make one common facility.
They say: "The intention for the site is to create one ownership with three facilities within, including - fine dining restaurant, bar and roof top bar with dining.
"The roof top bar will be screened with glass and aluminium construction to act as acoustic barriers.
"The open area is also to be set back from the Byres Road elevation to reduce the risk of noise leakage affecting the flats opposite.
"The roof area will have small trees and planting to the rear and to the front with a green roof included to create a mini habitat for birds and insects and provide a pleasant vista for the flats opposite and from the bathing club / gyms to the rear."
The plans say the roof bar will have a dedicated bar servery and will have covered areas for all-year-round use.
"It will be an asset for the thriving leisure / social scene of the local cosmopolitan community," the papers state.
"There is currently only one roof terrace nearby at the Chip on Ashton lane which is very popular with the customers and is busy throughout the year.
"This demonstrates a demand for this type type of facility in the neighbourhood."
The two garden areas will have "a green with grasses, sedum and plants again to encourage flora and fauna to populate the roof gardens".
The pavement outside the ground floor area is "wide and would support an external seated area without dramatically affecting the pedestrian users", according to the plans.
"The area will be bounded by 900mm high planters on wheels with a variety of flowers and flowering shrubs planted therein."
The papers say the site had approval for restaurant use and terrace at the front some years ago.
The site has been actively marketed for sale on this basis.
The papers state: "We hope this application will be looked on favourably."
Nico Simeone has opened a number of successful tasting restaurants in Glasgow, Edinburgh, and south of border in recent years.
His first restaurant 111 by Nico has just been taken over by his good friend and colleague Modou Diagne.
Fopp closed down at the start of this year in the midst of a changing music retail market.
Six By Nico Holdings Ltd declined to comment further on the plans.