The companies had been hoping to make an announcement as soon as this week, but it is not final, sources told CNBC’s David Faber.
Bloomberg first reported the news, citing people familiar with the matter who asked not to be identified since they were discussing confidential information.
The two companies could not be immediately reached by CNBC for comment.
Kroger is the largest supermarket operator in the country. It is made up of more than a dozen banners, including Fred Meyer, Ralphs, King Soopers, Harris Teeter and its namesake brand. It trails behind Walmart, which is the top grocer in the U.S. by revenue.
Kroger is the much larger of the two companies. Its market cap is about $32.6 billion compared with Albertsons, which has a market cap of $14.9 billion.
The talks come as competition in the grocery industry has intensified. About five years ago, Amazon spooked legacy grocers by acquiring Whole Foods. Its stores, which now include Amazon Fresh, still command a small percentage of the overall U.S. grocery market, but sparked a wave of investment.
Kroger, for example, struck a deal with British online grocer Ocado to build huge robot-powered fulfillment centers to pick and pack online grocery orders. It has used the new business model to break into new markets, including Florida. It also plans to expand in the Northeast.
The pandemic also pushed the industry to better cater to customer preferences, with services such as curbside pickup and home delivery. Yet those investments have also pressured grocers’ profits. Already, the grocery business is known for its thin margins and inflation has driven up the costs of food.
This story is developing. Please check back for updates.