Bristol-based Loungers Ltd has submitted the licensing application to High Peak Borough Council in respect of 22-23 Spring Gardens, which was formerly occupied by outdoor clothing retailer Trespass.
In its application, Loungers states the vacant unit is "to undergo a major refurbishment to form a new cafe/bar, Lounge".
An accompanying layout plan shows a trading area split over two floors, and includes a bar and cellar area on the ground floor, and a kitchen on the first floor. An area of outdoor seating is proposed.
The application states: "The operation will be a food-led, Continental-style cafe/bar. Opening will be all-day every day with the menu available throughout the day and evening.
"There will be a focus towards being family friendly with highchairs available, a selection of board games, daily newspapers and a free book swap facility. Music will be limited to background only."
Opening hours to the public, as requested, would be between 8am and 11.30pm, Sunday to Wednesday, from 8am to 12.30am Thursday to Saturday, and from 10am to 1am on New Year's Eve.
Members of the public have until March 8 to comment on the application.
A separate planning application requesting the change of use of the unit from retail to a cafe/restaurant has been submitted to the council and a decision is pending.
Loungers already operates sites in Derbyshire, including Pico Lounge at Glossop's Howard Town Shopping Park and Sorbo Lounge in Chesterfield.