The group's owner Hutton Collins is proposing to sell half of its current holding to investor Three Hills Capital Partners, which would become the majority shareholder.
The deal is subject to the successful restructuring of the business under the terms of a Company Voluntary Agreement (CVA), which could lead to the closure of up to 20 restaurants.
Accountacy firm KPMG, which is handling the restructure, confirmed the plans, which would see the sites pay a reduced rent for six months.
KPMG said that no restaurants would close on 'day one', and Byron would continue to pay employees, suppliers and business rates on time and in full.
The burger brand was sold to Hutton Collins for £100m in 2013 when it had just 34 sites, and it has since doubled its estate to almost 70.
Byron said in a statement that it would do ‘everything possible’ to find staff jobs at other sites in the event of closures.
It added that the restructure would allow it to ‘refocus the business on a smaller, more profitable core estate’.
“Byron’s core restaurant business and brand remain strong but the market that we operate in has changed profoundly,” said Simon Cope, CEO of Byron.
“In order to continue serving our loyal customer base, we need to make some critical and difficult changes to the size and shape of our estate.
“With the support of our new owners, our creditors, landlords and other business partners, I’m confident Byron will able to continue providing our consumers with the best burger experience.
“The teams in our restaurants are always such an inspiration and we will work hard to support them throughout this difficult process.”
Byron opened its first site in Kensington High Street in 2007 in a bid to bring US-inspired ‘proper hamburgers’ to the UK. It has been unable to escape the headwinds of rising costs hitting the casual dining industry, and placed four under-performing sites on the market last year.
The group has also faced beefed up competition from delivery rivals, UK brands such as Gourmet Burger Kitchen and an influx of American imports including Five Guys and Shake Shack.
Byron has submitted its restructuring plan to its creditors, who will vote on the CVA on 31 January.
Hutton Collins will retain a ‘significant minority interest’ in the group if the sale goes ahead.