Amazon is considering opening 3,000 of its cashierless stores by 2021, Bloomberg said in a report on Wednesday, based on conversations with people familiar with the matter. The e-commerce giant's push into retail would threaten the likes of convenience stores and fast-food chains across the U.S. selling items for customers in a pinch for time.

Amazon currently has three locations — known as Amazon Go — open in Seattle, where Amazon is headquartered, and on Monday opened a location in Chicago. The automated grocery stores promise "no lines, no checkouts, no registers." Customers simply scan their Amazon Go apps as they walk into the spaces — which are roughly 2,000 square feet — pick up whatever they want, and walk out.

"We don't comment on rumors or speculation," an Amazon spokesperson told CNBC in an emailed statement.

Shares of retailers including CVS, Walgreens, Walmart, Target and Kroger moved sharply lower Wednesday afternoon following the report.