(Reuters) - Macy's investor Arkhouse Management said on Thursday the U.S. department store was in talks with the investment firm for opening its books for due diligence on the prospects of a higher offer.

Arkhouse disclosed its move in a regulatory filing, saying this was in response to a letter from Macy's on March 11 that called the latest offer as "less than compelling" and that the board was "not prepared to transact at this price level".

The firm and Brigade Capital had on March 3 raised their offer to $24 apiece for the shares they did not already own, valuing Macy's at $6.6 billion, while leaving the door open for a higher bid.

"Negotiations with respect to the confidentiality agreement remain ongoing and Arkhouse Management and Brigade continue to await access to the requested diligence materials," Arkhouse said on March 14.

Arkhouse has a 4.4% stake in Macy's along with its affiliates. Macy's did not immediately respond to a Reuters request for comment.

"The fact the two sides are working on trying to reach an agreement signals a significant step in the discussions. Despite the movement, Arkhouse still intends to continue its proxy fight," a person familiar with Arkhouse's plans told Reuters.

The investment firm has nominated nine director candidates including executives with retail, real estate and capital markets experience, to the 14-member board of Macy's last month, kicking off a proxy battle.

Shares of the company were up 3.4% in early trading.

(Reporting by Savyata Mishra in Bengaluru and Svea Herbst-Bayliss; Editing by Arun Koyyur)