Over the past few months, talk has been building about Amazon (AMZN - Get Report) working on its own logistics service to compete against FedEx (FDX - Get Report) and UPS (UPS - Get Report)  , especially after the e-commerce giant recently confirmed it plans to lease a fleet of 20 jet airplanes. Now, FedEx has finally responded to the rumors.

During the shipping company's earnings call on Wednesday, FedEx CEO Mike Glenn brought up the Amazon rumors, calling them headline-grabbing but not realistic.

"While recent stories and reports of a new entity competing with the three major carriers in the United States grabs headlines, the reality is it will be a daunting task requiring tens of billions of dollars in capital and years to build sufficient scale and density to replicate existing networks like FedEx," he said.

Glenn also said that he's been aware of Amazon's need to ramp up its logistics capabilities, and acknowledged that Amazon is supplementing FedEx with its own services. But those investments don't mean that Amazon will stop using FedEx, he said.

"Amazon is a valuable customer that we've worked with for many years and we expect to work with them for many years to come," Glenn said.

And even if Amazon decided to stop using FedEx, the shipping company would still be fine, according to Glenn.

"No one FedEx customer represents more than approximately 3% of total revenue," he said. "We manage these relationships carefully to ensure we don't become overly dependent on any one customer."

While Glenn is certain, analysts are split on Amazon's ultimate logistics strategy.

After Amazon China registered to operate as an ocean freight forwarder in the U.S. in January, Baird analyst Colin Sebastian said "Amazon will not only build out its own transportation and logistics network, but also offer these as services to third parties." The strategy that Sebastian laid out mirrors the path Amazon took with Amazon Web Services, where it first built out cloud services for its own purposes, but later decided to sell those services to other companies.

Marc Wulfraat, founder and president of MWPVL, a supply chain logistics consultant, thinks that Amazon could be cutting out traditional carriers for some of its own deliveries, but will still need UPS and FedEx for locations where they do not have fulfillment or sortation centers, places like Wichita, St Louis, Dallas, and New Orleans.

ITG analyst Steve Weinstein agrees with Wulfraat.

"I don't know that they'll do 100% of the logistics themselves," said Steve Weinstein. "I expect them to keep finding opportunities, but I'm sure they will keep using third-party carriers as well." The traditional carriers do a good enough job, and Weinstein thinks Amazon will only step in to handle the delivery for unique opportunities, as opposed to across the board.

While Amazon hasn't commented on its larger logistics plans, it did comment specifically on its recent deal with Air Transport Services Group ATSG to lease 20 planes, making sure to note that it doesn't plan to stop using traditional carriers.

According to an Amazon spokesperson, "the planes provide critical capacity expansion to support the growth of Prime in the U.S. Planes provide an additional dedicated transportation method connecting Earth's largest selection to customers from coast to coast. At our scale, supporting growth requires adding some of our own logistics capabilities."