United Co-operatives has reportedly pulled out of the bidding war for Somerfield.
The Bristol-based retailer announced the co-op had decided not to make an offer for its business, but added it is still in talks with other potential bidders.
According to media reports, two groups are still in the running to buy Somerfield, which is expected to cost about £1.1 billion.
They include a consortium including Icelandic retailer Baugur, while the other involves property tycoons Ian and Richard Livingstone.
The Somerfield group includes 664 Somerfield stores and 560 Kwik Save outlets.
In May, United Co-operatives said it was looking at making a bid because it believed a deal would make "sound commercial, operational and financial sense".
However, in a statement this week, the group said it had decided not to proceed.
A spokesman said: “We said at the outset that this was not a must-do deal for us. We have had a look but have decided that it does not stack up for us.”
