WASHINGTON—The U.S. is examining ways to retaliate against Beijing’s restrictions on U.S. providers of cloud computing and other high-tech services, effectively opening a new front on its trade offensive against China.

According to individuals familiar with the administration’s thinking, the U.S. trade representative’s office is putting together a fresh trade complaint, probably under Section 301 of the Trade Act of 1974, arguing that Beijing unfairly restricts U.S. trade in these high-tech services.

The...