The business was its convenience store offshoot - known as M Local - before it was sold last September.
My Local has 1,650 staff in some 130 stores. New owner Greybull Capital lined up administrators on Tuesday.
Separately, Sir Philip Green plans to offer jobs to 1,000 workers who staff Arcadia concessions inside BHS, such as Dorothy Perkins and Wallis.
The news follows the collapse of BHS earlier this month, which put 11,000 jobs at risk.
Morrisons and Sir Philip have drawn up the separate plans to safeguard jobs after seeing their former businesses teeter towards closing.
Morrisons said in a statement: "If no buyer is found, and stores close, we will welcome our former colleagues back to a job at Morrisons."
A guaranteed job offer applies to those that worked at the chain when it was owned by Morrisons, although anyone hired in the interim will be considered.
The supermarket said it was "saddened and disappointed" by the news and said it wanted to "help our former colleagues who now work for My Local".
It was sold to investment firm Greybull for Â£25m in a deal fronted by retail veteran Mike Greene, who appeared on Channel 4 show The Secret Millionaire.
The chain has struggled to compete in the cut-throat grocery sector, which is embroiled in a bitter price war.
KPMG has been appointed as administrator for My Local. It will try to sell the company as a going concern, but if that is not feasible, it may sell the individual stores off in batches, or they may be closed down.
Sir Philip's plans for concession staff still leaves thousands of other BHS employees fearing for their jobs.
Last week, the billionaire apologised to BHS workers for the company's "sad" demise during a parliamentary hearing.
He has come in for criticism for the Â£400m in dividends taken out of the firm during his 15-year ownership, his management of the pension scheme, and the sale of BHS to former bankrupt Dominic Chappell, who had no retail experience.
The 163-store chain is in the process of being wound down by administrators.
The supermarket Morrisons has said it will offer jobs to most My Local staff in the event of the chain closing.