The heirs to the Nordstrom department-store chain are exploring a bid to acquire the company that bears their family name in a deal that would turn the publicly traded company into a private venture amid considerable turbulence for the sector.

The luxury retailer said Thursday that several members of the Nordstrom family, including multiple company executives, had formed a group to weigh the potential deal.

The potential shakeup comes amid a period of upheaval for department-store chains, which are facing declining mall traffic, intense online threats and cheaper, fast-fashion competitors. Department-store chains have announced hundreds of store closures in recent months.

Meanwhile, the luxury retail sector is also facing obstacles connected to the strong U.S. dollar, which is dampening tourist spending, and online threats.

About 23% of the company’s business is online, which is up from 5% a decade ago but still puts the company at significant risk as shoppers lose interest in the department-store experience.

Nordstrom has 122 full-line department stores in North America and 221 Nordstrom Rack stores, which are geared toward Millennial shoppers and people seeking high-quality discounted merchandise.

Family members interested in the acquisition recently told analysts that they believe their stores are in good shape and that…