The retailer Macy’s rejected a $5.8 billion takeover bid late Sunday that valued the struggling department store chain at roughly 20 percent above its closing share price on Friday, but suggested it was “open to opportunities.”

The bidders, Arkhouse Management and Brigade Capital, are seeking to acquire Macy’s stock they do not already own at $21 a share and have threatened to take the offer to shareholders.

With a potential hostile bid looming, questions are rising over how Arkhouse and Brigade could pull off a deal and whether additional suitors could appear, potentially setting off a bidding war.

In a statement released Sunday night, Macy’s board questioned whether the investment firms had the money to finance the deal, which it said “lacks compelling value.” It noted that the bid was accompanied by a letter with “numerous” untraditional stipulations.

Macy’s also questioned the deal’s financial feasibility. It said the firms had proposed to pay 25 percent of the offer in equity. The rest of the funding would likely come from debt such as leveraged loans, but appetite for such deals has waned thanks in part to high interest rates.

The unsolicited bid could draw others. Arkhouse’s 2021 offer for the developer Columbia Property Trust led to another buyer entering the picture and buying Columbia in a $3.9 billion deal.

Macy’s has not reached out to prospective buyers, people familiar with the matter said. But the retailer’s chairman and chief executive, Jeff Gennette, said in statement, “We continue to be open to opportunities that are in the best interests of the company and all of our shareholders.”

Still, list of prospective suitors is short, given the challenges facing the retail sector amid stubborn inflation and shifts in consumer spending. The detrimental effect of piling debt on a retailer in leveraged buyouts, like those for Payless, Toys “R” Us and Sears, have scared many private equity firms away from making such deals. Still, there may be some willing, particularly if attracted to Macy’s valuable real estate portfolio.

Macy’s has been under pressure to improve its business as consumers have spent less on discretionary items. Its shares have fallen about 30 percent over the past five years, as the company lost significant market share and was forced to close stores and lay off staff. Last week, it announced that it would cut 2,350 jobs.

Shares of Macy’s rose 3.4 percent on Monday morning.

As the company tries to turn around its fortunes, all eyes are on Tony Spring, who takes over as chief executive next month after having led Bloomingdale’s, Macy’s much-healthier, higher-end brand. But duplicating that success could be challenging: Macy’s shoppers are different than Bloomingdale’s customers, and it has a large and underperforming store base.

Jordyn Holman contributed reporting.

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