Regulators could block the takeover of Southern Co-operative by the Co-operative Group.
The deal, agreed in April, could reduce competition in some markets, says the Competition and Markets Authority.
The companies have a week to offer legally binding undertakings to address its concerns.
Southern Co-operative, based in Portsmouth, operates convenience stores – branded Food and Welcome – in the South of England including the counties of Hampshire and Dorset.
Founded in 1873, it has 300,000 members and 300 food, funeral and Starbucks coffee branches, including three crematoriums. However its profits have declined in the last three years.
Co-operative Group, which has seven million members, operates more than 2,500 stores – including many in the same regional markets as Southern Co-operative.