On Tuesday, My Local owner Greybull Capital announced its intention to put the firm into administration, lining up KPMG to act as administrator to its chain of more than 100 stores.
My Local was sold to Greybull last year by Morrisons and its previous owner has now said that if no buyer for the chain is found, it will offer its former staff jobs at the supermarket.
In a statement, Morrisons said: "We are saddened and disappointed to learn that My Local is about to enter administration.
"We want to help our former colleagues who now work for My Local.
"We can therefore confirm that if no buyer is found, and stores close, we will welcome our former colleagues back to a job at Morrisons."
KPMG will attempt to sell the business as a going concern but, if a buyer cannot be found, then the stores will be sold off piecemeal or closed down.
It is understood that Co-Op's convenience store arm has picked up five stores with Sainsbury's also acquiring one.
Greybull's acquisition of My Local was fronted by retail entrepreneur Mike Greene, who appeared on Channel 4 show The Secret Millionaire.
The collapse caps a torrid few months for the retail sector following on from the failures of BHS and Austin Reed.