Byron is understood to be seeking a buyer for the second time in less than three years.
The high street burger chain, owned by Famously Proper, it understood to have appointed Interpath Advisory to explore options for its future, as first reported by Sky News.
In August 2020 Byron was sold out of administration for £4m in a prepack sale, when Famously Proper took on 21 of its 51 sites.
Byron was founded in 2007 by the Gondola Group, which sold it in 2013 for a sum of £100m to private equity firm Hutton Collins.
Interpath Advisory declined to comment on the speculation.