Private equity firm Cerberus Capital Management LP and its partners are nearing a deal to buy parts of Supervalu Inc., The Wall Street Journal reported on Friday, sending shares of the grocery chain up 15 percent.

Cerberus and its partners will buy some assets of the company and take a stake in the remainder, which is expected to remain public, the newspaper said, citing a person with knowledge of the plan.

Cerberus would contribute around $500 million in equity, several hundred million less than initially discussed, the Journal said. A deal could be announced as soon as next week but could still fall through, the newspaper added.

Shares of Supervalu rose 39 cents to $2.98 on the New York Stock Exchange.

A Supervalu spokesman said on Friday the company's review of strategic alternatives was proceeding and that it was in "active discussions with several parties." He declined to comment further.

Cerberus did not respond to requests for comment.