The private equity owner of the 160-year old brand, Alteri Investors, has filed a notice to appoint administrators amid tough business conditions for the chain, which trades digitally and from 103 stores and concessions.
The decision is designed to give it some breathing space from creditors seeking to recover debts from the footwear and accessories retailer while it seeks a new owner.
While there is a risk of it falling into administration, Alteri and advisers KPMG are said to be talking to a number of buyers, with "credible" offers already on the table.
It is not known if those offers amount to a so-called pre-pack administration deal that would allow a new owner to ditch assets it does not want.
Alteri declined to comment.
It snapped up Jones Bootmaker - which began life in London in 1857 - and the Brantano brand in 2015, though Brantano UK collapsed just three months later following a poor Christmas.
It is believed that a turnaround plan for Jones Bootmaker had made some progress but a growing number of headwinds had severely dented that effort.
Those pressures include looming business rates increases, stiff competition and price rises linked to the collapse of the value of the pound since the Brexit vote which have lifted buying costs.