Like other legacy department store operators, Macy's has struggled to compete against younger, online competitors or peers with smaller brick-and-mortar footprints. This has given Arkhouse, a real-estate-focused investing firm, and Brigade, a hedge fund, an opening to put pressure on Macy's to explore a sale.

The two investment firms submitted a proposal last month to acquire the shares of Macy's they don't already own for $21 a share. The duo sees "the potential for a meaningful increase to the original proposal if we are granted access to the necessary due diligence," Arkhouse said in a statement.

But Macy's said the offer was not financially attractive or credible enough to grant such access.

"The board has determined not to enter into a non-disclosure agreement or provide any due diligence information to Arkhouse and Brigade," Macy's said in a statement.

Macy's also said that information furnished by Arkhouse and Brigade "failed to address its board's concerns regarding Arkhouse and Brigade's ability to finance their proposed transaction."

Macy's is not running a sale process with other parties and no other unsolicited bidders have emerged that meet the company's expectations about a potential deal, according to people familiar with the matter. Macy's expects a successful bidder to show enough committed financing and have a track record of pulling off buyouts in the retail sector, the sources added.

The Arkhouse and Brigade Capital Management-led investor group has a significant stake in Macy's through Arkhouse-managed funds, Arkhouse said.

Arkhouse said that investment bank Jefferies, which is acting as the buyout group's financial adviser, "has provided a highly confident letter supporting our ability to raise the necessary funds for the transaction."

Macy's, however, called the financing uncommitted and said it came with numerous non-standard preconditions.

The investment firms' bid has spotlighted how undervalued Macy's is relative to its real estate, which is projected by analysts to be worth between $7.5 billion to $11.6 billion.

Macy's owned 316 of its 722 total stores as of the end of January, according to its most recent annual report.

Macy's last week said it is cutting 2,350 jobs and closing five stores at it aims to streamline operations.