Sainsbury's and Asda are in advanced talks over a merger which would create a new supermarket giant.
The deal would be worth £10 billion and could be announced as early as Monday.
Asda is owned by the world's largest supermarket retailer Walmart and it is not yet clear how the deal would be structured.
One option is Sainsbury's absorbing Asda stores, while Walmart take a large stake in the combined group.
In a statement, Sainsbury's said: "J Sainsbury plc ("Sainsbury's") notes the speculation concerning a possible combination with Asda Group Limited.
"Sainsbury's confirms that it and Walmart Inc. are in advanced discussions regarding a combination of the Sainsbury's and Asda businesses. A further announcement will be made at 7am on Monday 30 April."
If Sainsbury's and Asda are to merge, together they would have a bigger share in the grocery market than Tesco.
The latest statistics show that Tesco has a 27.6% market share, while Sainsbury's has 15.8% and Asda has 15.6%. Together, they would move ahead of Tesco, with 31.4% of the market.
The merger would have to be approved by the Competition and Markets Authority (CMA), because the two entities are the second and third largest grocery retailers in the UK.
There is promise, however, that a deal could be approved after the CMA's decision to allow Tesco to take over Booker, the UK's largest grocery retailer in a deal worth £3.7 billion.
This would not be the first time Sainsbury's has acquired another high street giant. In April 2016, they announced a £1.4 billion takeover of Argos, which led to better than expected results the following Christmas.
The traditional high street has come under increasing pressure in recent years, with the growth in online retailers.
Sainsbury's and Asda have also been squeezed by the rise of lower-cost supermarkets Aldi and Lidl, who between them have a 12.6% grocery market share in the UK.