Kohlberg and Goldman Sachs Group's private-equity arm could make a bid by Monday, Women's Wear Daily reported.
The $52-a-share bid, which the newspaper said may or may not exclude Macy's debt, would represent a 30 percent premium over the stock's $40.03 closing price Tuesday, before the report was published.
The stock closed at $43.09, up $3.06, or 7.64 percent, Wednesday.
Macy's and Kohlberg spokesmen declined to comment on the report.
The newspaper said Kohlberg would want to keep Macy's management, including Chairman and Chief Executive Officer Terry Lundgren, who engineered Federated Department Stores Inc.'s purchase of May Department Store Co. in 2005. Federated changed its name to Macy's, after its flagship store, in June.
Sales at Macy's stores opened at least a year, fell 2.7 per cent in June, the company reported last week. The company also said earnings for the second quarter would be much lower than the year-ago period.
Macy's is headquartered in Cincinnati and operates almost 900 stores in the United States.