The Gap Inc. (GPS)

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Mr. West, who has 21 Grammy awards and whose Yeezy fashion brand had a tie-up with Nike Inc. and currently has one with Adidas AG, has talked about wanting to partner with Gap in various interviews over the years. He worked in a Gap store while growing up in Chicago and even rapped about the retailer in his 2004 song "Spaceship."

"I believe that Yeezy is the McDonald's and the Apple of apparel," Mr. West told The Wall Street Journal in March. "In order to make the Apple of apparel the next Gap, it has to be a new invention. To invent something that's so good that you don't even get credit for it because it's the norm."