BOISE — A $9.6 billion deal to buy Albertson’s Inc., the nation’s second-biggest supermarket chain, that appeared to have fallen apart three weeks ago might now be a possibility again.

A new bid has been submitted to Albertson’s board by the supermarket chain Supervalu Inc., and a consortium of private-equity investors, The Wall Street Journal reported Thursday, citing unidentified sources.

The new bid of just more than $26 per share was designed to reduce the antitrust worries blamed for halting the previous deal in December, the newspaper said.

That deal had Minnesota-based Supervalu trading stock and cash for hundreds of Albertsons stores that were doing well financially; and New Hyde Park, N.Y.-based Kimco Realty Corp. and a private-equity firm led by New York investment fund Cerberus Capital Management LP buying Albertsons stores not doing well financially for the price of the real estate.

CVS Corp., a Rhode Island-based company that has more than 5,400 retail and specialty pharmacy stores nationwide, was to buy Albertson’s pharmacy business for up to $4 billion.

That deal failed amid disagreements over who would be responsible if regulators, concerned with antitrust laws, tried to block the deal.

The most recent deal is devised to allay those concerns by eliminating some overlap between Albertsons and Supervalu in the Chicago area. Sources told the Wall Street Journal that the new deal has Supervalu selling its stores in Chicago to Cerberus and taking over the Albertsons stores.