Local official Abu Bakr bin Farid said Fahd al-Quso was killed Sunday, along with an aide, in an airstrike in the southern Shabwa province.
The Yemeni Embassy in Washington confirmed the report.
The airstrike resembled earlier American drone attacks, but the U.S. did not immediately confirm it.
Al-Quso was on the FBI's 10 Most Wanted Terrorists List since 2003. He was under indictment in federal court in Manhattan for the Cole bombing, and for an earlier attempt to bomb another U.S. Navy ship (the USS The Sullivans) with a second conspirator, Jamal al-Badawi.
Al-Quso and Badawi were jailed in Yemen, but they escaped.