The offer was made by investment firms Arkhouse Management and Brigade Capital.
But the department store chain said it had concerns over the valuation, and over the soundness of the financing.
Macy's is not running a sale process, and Reuters sources say no other unsolicited offers have emerged.
Arkhouse and Brigade already have a big stake in the firm.
They say investment bank Jefferies has vouched for their ability to fund the takeover.
But Macy's says their financial backing is not really committed, and comes with all kinds of non-standard conditions attached.
Some analysts say the bid just highlights how undervalued the company is relative to its real estate.
The portfolio of land and buildings is estimated to be worth up to $11.6 billion.
However, Macy's has been struggling to compete with younger online rivals, which has sapped its share price.
Arkhouse and Brigade felt that left the door open to a bid.
Last week, Macy's said it would shed 2,350 jobs and close five stores as it tries to streamline operations.
