The shift would represent a huge shakeup for the apparel industry, which has long been dominated by department stores like Macy's, Nordstrom, and JCPenney, as well as big-box retailers including Walmart and Target.
Amazon is a relative newcomer to the fashion world, and it has made a swift rise to the top.
The company's clothing and accessory sales are expected to grow nearly 30% next year to $28 billion, according to the Cowen analysts. Macy's apparel sales, by comparison, are expected to drop 4% to $22 billion in the period.
As Amazon's sales grow, so will its share of the apparel market in the US.
Amazon currently claims about 6.6% of the market. That share is expected to increase to 8.2% by next year, and further expand to 16.2% within five years, according to Cowen analysts.
By 2021, Cowen expects Amazon to generate $62 billion in annual apparel sales. TJ Maxx is expected to be the No. 2 clothing seller with $26 billion in sales and Macy's is expected to claim the No. 3 spot with $23 billion in sales.
Over the past couple of years, Amazon has ramped up its investment in fashion by launching its own private-label clothing brands and sponsoring the first New York Men's Fashion Week.
David Ramos/Getty Images
Macy's is losing market share to Amazon.
Also in the past few years, Amazon has started to shift its fashion strategy toward offering more high-end designer names, such as Zac Posen and Stuart Weitzman.
That shift has had some industry experts scratching their heads. Luxury fashion websites are typically well-merchandised and highly curated - not things for which Amazon is necessarily known.
Amazon's weaknesses with curation were highlighted in a shopper survey by Cowen & Co. that was conducted in July.
"Amazon Fashion got a very lukewarm review for site personalization and ease of use," Cowen analyst John Kernan said in a conference call Tuesday. Shoppers said it "wasn't particularly easy to browse."
Amazon also has the disadvantage of having no brick-and-mortar stores where shoppers can try on items or return purchases, he said.
So why do people choose to shop at Amazon for clothes?
Amazon Prime is the biggest lure for customers, according to Cowen.
Shoppers cited the convenience and free two-day shipping as the biggest advantage of shopping on Amazon for clothes.
Shoppers also praised Amazon's customer service and breadth of product reviews.
Disclosure: Jeff Bezos is an investor in Business Insider through hispersonal investment company Bezos Expeditions.