WASHINGTON—The Trump administration is nearing a offer with Sudan to solve claims around al Qaeda’s 1998 bombings of U.S. embassies in Africa, aiding apparent the way to eliminate Khartoum’s designation as a state sponsor of terrorism.

The approach is component of U.S. attempts to help the civilian-led transitional govt in Sudan, whose armed forces previous calendar year ousted President Omar al-Bashir, a military services dictator who seized electric power in 1989. Before this calendar year, Sudan settled terrorism-connected claims from the 2000 al Qaeda suicide bombing…