Albertson’s Inc. on Friday confirmed that it received a new bid to purchase the entire company from a consortium that had previously submitted an offer, in a deal that has been valued at about $9.6 billion.

The Wall Street Journal reported on Thursday that the consortium led by private equity fund Cerberus Capital Management LP, along with real estate investment fund Kimco Realty Corp. and Minneapolis-based discount grocery group Supervalu Inc. offered about $20 in cash and $6 in Supervalu shares. In total the bid was worth a few cents more than $26 a share.

Albertson’s on Friday did not disclose what companies were in the consortium or what the total offer was worth. But Supervalu said in a statement that it had resumed discussions with Albertson’s regarding an acquisition by a consortium of investors that includes the grocer.

After reviewing the new proposal Albertson’s board authorized management and its representatives to enter into negotiations. The company emphasized that there can be no assurances that any transaction will occur as a result of these negotiations.

The new bid includes a structure designed to lessen antitrust worries, which had derailed a deal that was just hours away from completion in late December, the Journal said.

The Cerberus-led consortium became the lead bidder for Albertson’s after the supermarket chain said in September that it was exploring the sale of all or part of its business.

The deal was to be linked to one in December in which drugstore chain CVS Corp. was going to buy Albertson’s 695 free-standing Osco and Sav-on drug stores for as much as $4 billion. The group led by Cerberus was going to buy groups of poorly performing Albertson’s stores for the value of their real estate; Supervalu was going to swap stock and cash for hundreds of Albertson’s better-performing stores, the Journal said.

Just before Christmas, the deal failed over disagreements as to who would accept responsibility if regulators tried to block the deal because of antitrust concerns.

Under the original plan, the buyers would also be shouldering $6.1 billion of existing Albertson’s debt and an additional $3.8 billion to pay cash to Albertson’s shareholders. Supervalu also intended to issue stock that would give Albertson’s shareholders ownership of more than one-third of the combined company.

It’s unclear how the new deal would overcome the prior antitrust concerns.