According to Sky News, Mohsin and Zuber Issa wrote to Caffè Nero over the weekend to propose buying the coffee chain from Gerry Ford - its founder and controlling shareholder.
Ford, who founded Caffè Nero in 1997, confirmed earlier this month that the business had launched a Company Voluntary Arrangement (CVA) in response to the 'decimation' in trade caused by the ongoing Coronavirus restrictions.
The group, which employs more than 6,000 people across 800 stores, appointed KPMG to advise on the CVA with a view to renegotiating rent agreements with landlords and reduce costs.
Under the EG proposal, Caffe Nero's landlords would be paid in full for the rent arrears owed to them as a result of the Covid-19 crisis.
People close to the situation say that represents a significant improvement for the chain's store-owners over the CVA proposal on which they are scheduled to vote on today (30 November).
It was unclear whether Caffe Nero had responded to the EG offer yet, or what the precise terms of the offer were.
EG's bid could force the coffee chain to postpone the CVA vote, insiders said.
Both parties declined to comment.