Morrisons said if no buyer came forward, it would take on staff left out of work as a result of branch closures.
Today Mike Greene said he was "truly sorry" that he and his management were unable to save the business.
"The last nine months has been one of the toughest retail trading periods that I have ever experienced and My Local has faced intense competition."
"The management team has been unable to return the business to profitability. For that I am truly sorry."
KPMG's Mark Orton said discussions over sales of the remaining stores were "active".
"We are pursuing these opportunities as a matter of priority in the hope that we will be able to conclude successful sales and safeguard as many jobs as possible."
Morrisons made a loss of around £30 million when it sold the fleet of convenience stores as part of chief executive Dave Potts' plans to refocus the Bradford-based grocer on its core supermarkets.
Back to basics: David Potts
Toby Melville/Reuters
Potts said Morrisons, which arrived late in the convenience sector, had been unable to scale the chain.
Orton said the convenience sector has been suffering from "significant challenges in recent times, through increasing competition, pricing pressures, changes in customers’ buying habits and general structural change within the sector".
KPMG highlighted Local Data Company figures showing convenience stores were the slowest growing segment in the food and groceries market over the last five years.
