The move reflects a decision by new CEO David Potts to go back to basics and focus on the core supermarket estate.
The Sunday Telegraph reported that Bradford-based Morrisons is in “advanced talks” to sell its convenience stores to investment firm Greybull Capital, which rescued Monarch Airlines last year.
Both Morrisons and Greybull declined to comment.
The opening of M Local stores under Mr Philips was designed to cash in on the growing popularity of convenience stores at a time when many shoppers were ditching their cars amid rocketing petrol prices.
However the price of oil has fallen significantly over the past year, making driving affordable once more.
While convenience stores remain a growth sector in sales terms, there are doubts about how profitable they are.
This is particularly the case at Morrisons, which was heavily criticised for paying over the odds for stores that were in the wrong place.
Earlier this year Morrisons announced plans to close 23 of its M Local convenience stores with the loss of 300 jobs. Chairman Andy Higginson said a third of the convenience store portfolio had failed.
Morrisons has around 160 convenience stores which generate around £300m in sales a year.
The move comes as arch rival Leeds-based Asda prepares to announce trading figures on Tuesday following a run of declining quarterly sales.
Last month the supermarket chain saw rival Sainsbury’s overtake it to reclaim its position as the UK’s second largest grocer for the first time since January, according to Kantar Worldpanel.
Asda has been very clear about its strategy in that it won’t join in the short term vouchering of its rivals.