The Trump administration is weighing new trade restrictions on China that would limit the use of American chip-making equipment, as it seeks to cut off Chinese access to key semiconductor technology, according to people familiar with the plan.

The Commerce Department is drafting changes to the so-called foreign direct product rule, which restricts foreign companies’ use of U.S. technology for military or national-security products. The changes could allow the agency to require chip factories world-wide to get licenses if they...