According to published reports, Kroger, the largest supermarket chain in the U.S., recently approached Safeway about buying part of its operations. The reports also said that Kroger contacted Cerberus Capital Management, the private equity firm that is considered the favorite to purchase Safeway, about buying some stores that Cerberus may not want.

Cerberus led the investor group that purchased Supervalu last year. Safeway recently closed its 72 Dominick’s stores in the Chicago area, sold its Canadian business, and in the last couple years sold or closed all but one of its Genuardi’s stores.

Experts speculated that an arrangement between Kroger and Cerberus could help address antitrust concerns that could arise in select markets if one of the companies purchases Safeway.