Delivery company shares are dropping as investors worry Amazon is about to disrupt the industry.

Shares of UPS fell more than 0.7 percent Thursday. FedEx dropped as much as 1.6 percent before closing 0.1 percent higher.

Bloomberg News is reporting Amazon is trying out a new delivery program called "Seller Flex" where the company will pick up packages from third-party sellers selling on its platform and deliver the products to consumers.

Amazon clarified that the offering will continue to use some of its current delivery partners, but didn't comment on whether it will increase its own deliveries directly to customers.

"We are using the same carrier partners to offer this program that we've used for years, including UPS, USPS and FedEx," Amazon said in a statement.

One analyst believes a big expansion by Amazon into the delivery business is inevitable.

"Given the investments that Amazon is making in fulfillment infrastructure and transportation to support its own retail business, we view it simply a matter of time until they offer these services to third parties more broadly," Baird analyst Colin Sebastian wrote in an email. "This is the same strategy that Amazon has successfully utilized in retail (third party marketplace) and technology (AWS) where they offer as a service the same platforms built to run their business."