A source close to the supermarket said 'M Local' and 'Morrisons Local' were two options currently being tested.
Several designs have been created, based on Morrisons' yellow-and-green branding. The source said: "Morrisons will make final decisions on the brand name and image in the next couple of months."
A Morrisons spokesman would not be drawn on details of the branding or whether the first store would open this year, adding plans were "still at an early stage".
Last September, chief executive Dalton Philips said he predicted a "real opportunity" in convenience stores.