The reports come just weeks after the Issa brothers and their private equity backers, TDR Capital, landed an agreement to buy Britain's third-largest supermarket, Asda, for £6.8 billion from Walmart.
The brothers have grown the Lancashire-based EG Group into a huge private company with a network of around 6,000 petrol forecourts around the world.
Evening Standard has contacted Caffe Nero and EG Group for comment.