Morrisons bought the 1,100 store McColl's for a reported £190 million ($210 million) in May after it collapsed into administration.
However, the Competition and Markets Authority (CMA) launched an investigation into the deal in July.
Following an initial probe, the watchdog found the deal would not harm the vast majority of UK shoppers or other businesses, but that it raised competition concerns in 35 areas.
To address these concerns, Morrisons offered to divest 28 McColl's stores.
The CMA said it was minded to accept these proposals.
"The CMA is now consulting on the proposals – known as undertakings – for the sale of these stores. If the CMA accepts the proposals, the deal would be cleared to proceed," it said.
The 500-store Morrisons has been owned by private equity firm Clayton, Dubilier & Rice (CD&R) for a year.
CD&R is also the parent company of the Motor Fuel Group, which owns more than 800 convenience stores.
Third Quarter Earnings
Morrisons last month reported a halving of third-quarter core earnings against the backdrop of a cost of living squeeze.
It has also lost its place at Britain's fourth largest grocer to discounter Aldi.