WASHINGTON—The Trump administration is preparing to initiate direct talks with Iran-backed Houthi forces in Yemen in an effort to end the four-year-old war, a conflict that has become a volatile front line in the conflict with Tehran, according to people familiar with the plans.

The U.S. is looking to prod Saudi Arabia into taking part in secret talks in Oman with Houthi leaders in an effort to broker a cease-fire in Yemen, according to these people.

The...