It was reported back in May that the business had appointed restructuring firm Quantuma to advise it on seeking new rent terms, but the group is now understood to be exploring a CVA proposal in response to the pressures caused by the second national lockdown in England.
According to Sky News, the CVA arrangement would likely to involve seeking permanent rent cuts from landlords.
Plans are reportedly at an early stage and the implications for store closures and potential job losses are yet to be disclosed.
“As a result of this second lockdown our sales are 70% below last year and this is unsustainable,” co-founder John Vincent told The Times.
“In light of this, the most likely and constructive way to move forward with our landlords is through the framework of a CVA.
“We stayed open to serve NHS and other key workers throughout this pandemic. Once everyone else returns to city centres and travel hubs we fully expect Leon to grow again.”
Founded in 2004 by Vincent and Government 'food tsar' Henry Dimbleby, Leon operated 75 sites across the UK prior to the pandemic.
It also operates global locations in Washington DC, Oslo, Amsterdam, Dublin, Rotterdam and Gran Canaria.
The slower-than-expected return to offices in city centres has had a severe impact on high street operators.
In September it was reported that fellow high street coffee chain Costa had warned that up to 1,650 jobs across its estate were at risk of redundancy as a result of the ongoing impact on trade caused by the pandemic.
Meanwhile, last month Pret A Manger announced it was to close a further six sites and cut around 400 more jobs after its recovery was hampered by a tightening of Coronavirus restrictions and rising case numbers.
The sandwich chain had already shuttered 30 of its branches and made 2,800 staff redundant earlier in the summer as part of a major restructuring of the business.
Last week, Caffè Nero launched a CVA in response to the 'decimation' in trade caused by the ongoing Coronavirus restrictions.
Chief executive Gerry Ford said the high street coffee chain had lost vast amounts of trade as a result of city centre office workers being told to work from home.
It is hoped that the number of site closures and job losses will be minimal.