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The offer, announced Monday, is being led by Hudson's Bay Executive Chairman Richard Baker, Rhone Capital LLC, WeWork Property Advisors, Hanover Investment SA and Abrams Capital Management. The proposal values the company at 9.45 Canadian dollars ($7.12) per share.
Together, the group of shareholders owns a majority 57 percent of the company.
"We believe that improving (Hudson's Bay's) performance will require significant time and patient long-term capital that is better suited in a private company context without the emphasis on short-term results and returns," said Baker in a statement.
The offer is conditioned in part on the $1.5 billion sale announced Monday of Hudson's remaining half of its interest in its European business.
Hudson's Bay Company owns brands like its namesake Hudson's Bay, Home Outfitters, Lord & Taylor and Saks Fifth Avenue.
The company said a special committee of independent directors will review the shareholders' privatization proposal and oversee a formal valuation.
"The Special Committee noted that no decision has been made and it intends to carefully and thoroughly review the proposal with the assistance of its outside financial and legal advisors. There can be no assurance that any definitive agreement will be executed or that the proposed transaction will be approved or consummated," Hudson's Bay said in a statement.
The retailer group's stock jumped more than 44 percent and closed at $6.85 per share following news of the proposal.
Like many department stores, Hudson's Bay has struggled to adapt to a dramatic shift to online shopping.
Last month, Hudson's Bay said it hired a financial adviser to review its Lord & Taylor's business, which it acquired in 2012, and that the process may lead to a sale or merger.
The move follows the closing of the Lord & Taylor flagship on Manhattan's Fifth Avenue in early January after the building was sold to WeWork, an office space-sharing company.
The Associated Press contributed to this report.