Shares of Nordstrom tumbled 3 percent in early morning trading Monday after the stock was downgraded as same-store sales at the upscale retailer’s brick-and-mortar locations decline and its chain of discount stores, Nordstrom Rack, comes under pressure.

Cowen and Co. lowered its rating to market perform from outperform and dropped its share price target to $51 from $56 and warned that the retailer may need to close up to 10 percent of its physical stores as more consumers shop online. The stock ended Friday at $51.78, having climbed about 9 percent so far this year. Nordstrom has a market value of about $8.7 billion.

The company’s off-price division, Rack, “remains a work in progress as digital strength has masked weak physical store comps,” Cowen analyst Oliver Chen said in a research note Monday. He said same-store sales at Nordstrom Rack have declined for the past six quarters, underperforming other off-price rivals like Ross Stores and TJX.

“Meanwhile, both an opportunity and risk is recent leadership turnover at Rack with the re-introduction of Geevy Thomas as President of Nordstrom Rack following the retirement of Karen McKibbin,” Chen said.

Analysts and investors continue to wonder if a premium should be paid above the $50-per-share offer that was on the table earlier this year, when the department store chain was trying to go private. A special committee advising Nordstrom’s board ultimately ended talks with the Nordstrom family about those efforts, after the two parties couldn’t agree on price.

The Nordstrom family had hoped that, after going private, the company could further its digital investments and focus on realigning its store footprint, sources previously told CNBC.

According to Chen, Nordstrom will likely need to close more stores in the long term, though the retailer does have a “significantly healthier physical store fleet” compared with Macy’s and J.C. Penney. (Nordstrom has 122 full-line stores and 239 Rack stores, while Macy’s has nearly 700 stores under various banners across the U.S. and J.C. Penny has more than 850.)

Nordstrom could close up to 10 percent of its stores, bringing its footprint to roughly 110 locations in the most profitable malls and putting the company in a better position to focus on e-commerce, Chen said.

Showing it was more serious about making investments online, Nordstrom earlier this year acquired two digital start-ups — BevyUp and MessageYes. The company meanwhile has been testing a store in California without any inventory — instead, the location, known as “Nordstrom Local,” focuses on experiences. In New York, Nordstrom just opened up its first store dedicated to men and will open a full-line store, right next door, for women next year. (It previously only operated Rack locations in the city.)

Nordstrom is holding its analyst day on July 10, where management is expected to update the financial community on its strategy and any new initiatives.

The company’s stock could pop if executives convince analysts that they can improve sales and profit margins at Nordstrom’s brick-and-mortar stores, Chen said. Investors will also be looking for any news on the dividend or a new share buyback program, he said.

— CNBC’s Lauren Hirsch contributed to this report.