The Trump administration, deepening its global trade offensive, is preparing to levy tariffs on tens of billions of dollars of Chinese goods in the coming week, perhaps as early as Friday—a move that is likely to spark heavy retaliation from Beijing.

Senior trade officials in the White House, the Commerce and Treasury departments and the U.S. Trade Representative’s office met on the issue before President Donald Trump went to a summit of the Group of Seven industrialized nations in Canada on Friday—and agreed that the U.S....