The U.S. and China are closing in on a deal that would give China’s ZTE Corp. a reprieve from potentially crippling U.S. sanctions in exchange for Beijing removing tariffs on billions of dollars of U.S. agricultural products, said people in both countries briefed on the deal.

The negotiations also would ease roadblocks in China faced by U.S. semiconductor company Qualcomm Inc., whose proposed acquisition of NXP Semiconductors NV of the Netherlands has been held up by Beijing. China’s Commerce Ministry has pledged to immediately...