Despite competition from e-commerce giant Amazon, Stitch Fix is committed to remaining independent. And at Recode's 2018 Code Conference in California, CEO Katrina Lake said the young clothing subscription company has never seriously discussed a buyout from Amazon.

"We haven't had any serious discussions about combining the companies," she said on Wednesday.

Amazon has long hosted clothing items on its e-commerce platform, but the June 2017 launch of Prime Wardrobe positioned the company to be a direct competitor to online fashion companies, like Stitch Fix and Trunk Club. Included with all Prime memberships, Prime Wardrobe includes brands outside of Amazon's private labels, like Adidas, Calvin Klein, Levi's and Hugo Boss.

Although Amazon has indisputably disrupted retail, Lake argued the business model is "almost the opposite" of Stitch Fix. Whereas Prime gives shoppers "literally millions of things to choose from," Stitch Fix sends five items, Recode reported.

"It's a very select group of things that we think are highly relevant for you. That discovery is sometimes the hardest part of apparel," Lake said.

Lakes remains confident about taking the company public in November 2017, and the path Stitch Fix has taken since then.

"Right now we feel really confident on the path that we're on," she said.