Amazon's next big move could be taking on the giants of the delivery industry, RBC Capital Markets' Mark Mahaney told CNBC on Thursday.

"There's another investment cycle coming, and I bet you it's around shipping and them actually coming out and directly competing with FedEx and UPS," the lead internet analyst said on "Power Lunch." "I think it's just a matter of time before that happens and it will be an investment cycle in front of that."

Mahaney called Amazon "the best revenue makeshift story in tech" because its cloud and advertising segments have margins tenfold the size of its retail business. The company is in position to reach all-time highs, he said.

"You can now think about this company as being a double-digit operating margin company," Mahaney said. "You couldn't have thought that over the last 20 years that I've been covering this company."

The internet giant recently said it would deliver packages for free during the holiday shopping season. That comes at a time when wages and shipping costs have been rising.

"Knowing Amazon, I wouldn't be at all surprised to see them be willing to take down margins that they thought could really get a boost in terms of customer loyalty, more Prime customers, etc.," Mahaney said.

Rumors have swirled that Amazon would get into the delivery business since 2016. The Seattle-based online retailer most recently made strides in delivery and logistics with its own last-mile Delivery Service Partners. The tech firm has also established Amazon Flex delivery in more than 50 cities across the country.

FedEx, which says shipments from Amazon make up about 3 percent of its revenue, has downplayed the nascent delivery service, saying it's not a match to the infrastructure the shipping giant has built up over more than four decades.

Amazon has said its shipping costs, which continue to rise, have spiked from $11.5 billion in 2015 to $21.7 billion in 2017.