Cerberus Capital Management is reportedly looking to wrap up a $9 billion deal for Safeway (SWY) this week, while rival grocery chain Kroger (KR) considers a possible bid.

Safeway revealed last month that it was speaking to potential buyers, calling the conversations “ongoing.” The Pleasanton, Calif., company also reported stronger-than-expected earnings for the fourth quarter.

According to The Wall Street Journal on Wednesday, private equity firm Cerberus offered to buy out Safeway for $40 a share.

The private equity firm had hoped to finish the deal earlier this week, but Kroger’s interest threw a wrench into those plans, the report said.

Early last year, Cerberus struck a $3.3 billion deal to buy five grocery brands from Supervalu (SVU), including the Albertsons stores it didn’t already own. Cerberus intends to pair Albertsons supermarkets with Safeway.

Kroger is said to be considering a bid for all or part of Safeway, the nation’s second-largest grocery chain. Sources told the Journal that Cerberus remains the favorite, considering possible antitrust risks in a tie-up between Kroger, the top grocery chain, and Safeway.

Kroger declined to comment. Spokespeople for Safeway and Cerberus didn’t immediately respond to requests for comment.

Shares of Safeway climbed 1.9% to $39.37. Kroger was also trading 1.9% higher to $43.18.

Follow Matthew Rocco on Twitter @MatthewRocco