Arkhouse Management and Brigade Capital Management submitted a proposal at the beginning of the month to take Macy's private for $5.8 billion, according to a story in the Wall Street Journal weekend that cited people familiar with the matter. The two companies, which already have a big position in the department store giant, offered to buy the Macy's stock they don't already own for $21 a share, representing a 32% premium to where shares closed the day before.

According to the Wall Street Journal, it isn't clear how the retailer views the proposal. The publication also reported that the investor group believes Macy's is undervalued in the public markets and would be willing to raise its offer subject to due diligence.

The deal would have a significant impact on the retail landscape given Macy's heft. It operates nearly 500 department stores under the Macy's name, as well as Bloomingdale's, which has more than 30 locations, and a number of discount and smaller-format shops under the two banners, according to the WSJ.