March 4 (Reuters) - Macy's shares jumped 16% before the bell on Monday after investors Arkhouse Management and Brigade Capital sweetened their take-private bid over the weekend, valuing the U.S. department store operator at $6.58 billion.

They raised the offer price to $24 per share for the remaining stake that they do not own from $21 per share. The retailer's shares, which had lost 10% last year, rose to $21 following the latest bid.

"We remain open to increasing the purchase price further subject to the customary due diligence," Arkhouse had said on Sunday.

Macy's is yet to open its books to the bidders as it was reviewing the new offer after rejecting in January a prior bid from Arkhouse on concerns around deal financing and valuation.

The real estate-focused investing firm has now said it has identified global lenders who will commit to financing the deal if due diligence was granted.

"Macy's should cooperate with the investment group and pursue a possible sale. If it refuses to do so, it runs the risk of a hostile takeover," said David Swartz, an analyst with Morningstar Research.

The company has struggled to maintain its sales growth and profitability amid competition from cheaper physical and ecommerce offerings and a value-based shopping pattern due to elevated inflation and higher borrowing costs.

It last week unveiled a turnaround plan that included cutting store counts and job roles, while aiming to revive sales at its luxury labels Bloomingdale's and Bluemercury by improving merchandise and adding more staff.

Arkhouse, which has an economic exposure of 4.4% to Macy's along with its affiliates, has piled pressure by nominating nine director candidates with retail, real estate and capital markets experience to the company's 14-member board.

Macy's forward price-to-earnings multiple, a common measure for valuing stocks, is 6.73, lower than industry peers, including Kohl's and Nordstrom that have a P/E ratio of 10.36 and 10.28, respectively. (Reporting by Savyata Mishra in Bengaluru; Editing by Arun Koyyur)