SuperValu shares rose slightly on Monday after a Reuters report cited people familiar with the matter as saying some of the world’s largest buyout firms are preparing offers for the company’s Save-A-Lot business.

Private equity firms Advent International Corp, KKR & Co. LP (KKR) , Clayton, Dubilier & Rice LLC, TPG Capital LP, Onex Corp and Thomas H. Lee Partners LP are participating in an auction for Save-A-Lot, the people were cited as saying in the news report.

Some of the firms could make binding offers that would value Save-A-Lot at as much as $1.8 billion, the people stated in the report. Supervalu is expected conclude the auction in the coming weeks and decide whether to sell Save-A-Lot outright or spin it off to Supervalu shareholders, the sources added.

The sources cited in the report asked not to be identified because the deliberations are confidential, according to the news report. Supervalu did not immediately respond to a request for comment. Representatives for the private equity firms either declined to comment or did not respond to requests for comment.