As FedEx Corp. stops shipping Amazon.com Inc. packages, United Parcel Service Inc. mulls a similar question to the one its delivery rival just faced: grow alongside one of the world’s largest shippers or cut off a looming competitor?

For now, UPS is retaining close ties to Amazon, one of its largest customers. The Atlanta-based shipping giant gets close to 10% of its revenue from Amazon, according to a Morgan Stanley estimate, a figure that could grow as the online retailer seeks new carriers for the packages that once went to FedEx.

The decision could pose risks down the road, if Amazon is able to build out its own delivery network enough that it can cast aside UPS, the U.S. Postal Service and any other regional shippers. Losing that big a customer could hurt UPS by depriving it of a large chunk of revenue and volume to fill—and pay for—its vast package-delivery network.

But UPS currently retains some power in the relationship, especially as Amazon nears the all-important holiday shipping season, when it will have to lean on outside carriers to meet its shipping needs.

“Amazon doesn’t have anyone to turn to right now to replace UPS to the extent they need to,” said John Haber, chief executive of supply-chain consulting firm Spend Management Experts.