WASHINGTON—The Trump administration’s proposed crackdown on China’s trade practices could hit one sector where the U.S. runs a big trade surplus: higher education.

The White House is considering limiting visas to Chinese students as part of a broad package of measures targeting Beijing, which the U.S. accuses of violating intellectual-property laws and other misdeeds. A White House official said the package, including tariffs, could be unveiled later this month.

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