A group of Nordstrom family members that own 31.2% of Nordstrom have been working on a proposal to increase their stake in the department store to more than half, The Wall Street Journal reported on Thursday.

The family last year aborted talks to take the retailer private after an initial offer of $50 a share was rejected as too low. Shares of the retailer have in recent weeks slipped nearly $20 below that offer.

Shares of Nordstrom were up more than 8% on Thursday, giving it a market capitalization of $5 billion, according to Factset. Year to date its shares are down nearly 30%.

The company has been swept up in a wave of investor doubt that has also hit peers Macy's, J.C. Penney and Kohl's. Investors have questioned whether there is a continued need for department stores, as more shoppers head online or buy from brands directly.

But Nordstrom — with its affordable luxury price-point and high-touch customer service — has long been viewed as the darling among department stores. It has fewer stores than competitors like Macy's, which is a benefit as shoppers increasingly head online. It continues to have strong relations with brands, as others struggle to lure them into their stores.

Its off-price retail concept, Nordstrom Rack, is a roughly $5 billion business that has recently slowed, but benefits from the same bargain shopping trends that have sent shares of TJ Maxx parent TJX up nearly 23% year-to-date.

With the family holding a larger stake in the company, it would be less subject to investor whims as it focuses on transforming its business to match today's shopping habits. Those endeavors include include a New York flagship set to open in October, which it reportedly spent north of $500 million to build.

Earlier this year, one of the controlling family members, 58-year-old Blake Nordstrom, unexpectedly passed away. He had been working as co-president and was active in its day-to-day operations, people familiar have told CNBC.

A spokesperson for Nordstrom declined to comment on the report.