An investor group has made a $5.8 billion offer to buy Macy’s, in a bid to take the famed department-store chain private after stiff competition from online rivals took a big bite out of its value.

Arkhouse Management, a real-estate focused investing firm, and Brigade Capital Management, a global asset manager, on Dec. 1 submitted a proposal to acquire the Macy’s stock they don’t already own for $21 a share, people familiar with the matter said.