The chain, which has 125 stores in the UK, cited tough market conditions across the sector.
In September 2015, supermarket group Morrisons sold My Local stores to a team led by retail entrepreneur Mike Greene and backed by investment firm Greybull Capital.
Ninety of the company's 125 stores have closed while three more are in the process of being shut, KPMG said.
Employees in sold stores will be transferred to the new owners and Morrison will employ former workers in case a store is closed, My Local said.
KPMG is in discussions with interested parties for the remaining 32 trading stores.
"Companies across the convenience store sector have faced significant challenges in recent times, through increasing competition, pricing pressures, changes in customers' buying habits and general structural change within the sector," KPMG partner Mark Orton said.
(Reporting by Bhanu Pratap in Bengaluru)
