The Trump administration is examining whether to require that next-generation 5G cellular equipment used in the U.S. be designed and manufactured outside China, according to people familiar with the matter. The move could reshape global manufacturing and further fan tensions between the countries.

A White House executive order last month to restrict some foreign-made networking gear and services due to cybersecurity concerns started a 150-day review of the U.S. telecommunications supply chain. As part of that review, U.S....