The deal, being brokered by its owner Calveton alongside advisers at Interpath Advisory, could be announced later this week, according to Sky News.
Last week it was announced that Famously Proper, which owns Byron and fried chicken concept Mother Clucker, had filed a notice of intention to appoint administrators, but that it was looking to progress a transaction that would support the business in the long term.
It comes after the group appointed Interpath Advisory to review its options back in November.
The news marks the third time in less than five years that the Bryon brand has undergone a restructuring.
The group, which was generating annual sales of £90m from more than 70 restaurants at its peak, was acquired by Famously Proper from pre-pack administration in the summer of 2020 through private equity firm Calveton UK Limited.
Famously Proper went on to acquire Mother Clucker in May 2021. It subsequently launched a bricks and mortar site under the brand in London's Islington, but that restaurant now appears to have closed. Mother Clucker does continue to provide a delivery service through the Byron estate, however.
Byron first restructured in 2018 through a Company Voluntary Agreement (CVA) that resulted in the closure of almost a third of its 70-strong estate. The pre-pack deal in 2020 resulted in a further 31 restaurants closing.