Sources cited by the magazine said KKR, which has filed for an initial public offering, was partnering with Goldman Sachs & Co. on an offer valued at $52 a share, or about $24 billion, and which may or may not exclude Macy's debt.
Macy's shares closed on Tuesday at $40.03.
Women's Wear Daily quoted private equity sources as saying an agreement in principle could be ready within days and that parties may be aiming to get details ironed out before Monday, the scheduled date for a series of investor meetings planned by Macy's management.
The magazine said the deal was seen as a way for KKR to help boost interest in its shares upon completion of its initial public offering, slated for later this year.
Current Macy's management, including Chairman and Chief Executive Terry Lundgren, would probably remain in place after a KKR takeover, the magazine said.
Macy's, which also operates the Bloomingdale's chain, is an attractive takeover target for the veteran buyout firm because it has a well-known brand, generates cash, and owns 54 percent of its real estate, said the magazine.
Neither Macy's nor a KKR representative were immediately available for comment.