The prominent Burlington Street shop is up for let by Rob Alston Retail.
Burton was founded by Montague Burton in Chesterfield in 1904 under the name of The Cross-Tailoring Company.
The firm is one of the UK’s largest men’s fashion retailers with more than 400 stores in the UK and Ireland.
The Derbyshire Times asked Burton why the store may be shutting, if any jobs are at risk and why the company is considering closing its founding shop.
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However, a Burton spokesman simply said: “At the moment we do not have any further comment to add to this.”
Rob Alston Retail states the store would be suitable for a restaurant.
The property has a ten-year lease and rent of £65,000-per-year attached to it.
Last year, Burton announced it was opening an outlet in Chesterfield Tesco.