The Trump administration is weighing whether to place export restrictions on China’s most advanced manufacturer of semiconductors, a move that could cut to the heart of China’s ambitions to become self-reliant on critical technologies.

U.S. agencies are in discussions to determine whether Semiconductor Manufacturing International Corp. should be added to the Commerce Department’s “entity list,” a step that would require companies to go through a difficult layer of review before exporting any U.S. technology to SMIC, said a…