A spokesman for the Joint Task Force hunting members of Boko Haram said Monday Abu Qaqa and Isah Abuja, were killed in a firefight at a police checkpoint, the Leadership newspaper reported.
JTF spokesman Lt. Col. Ikediche Iweha said Qaqa and Abuja were taking Abuja's wife for medical treatment when they were stopped at a checkpoint. Rather than risk being identified, the men began firing at officers manning the station.
Qaqa and Abuja were killed in the ensuing clash, Iweha said. The woman was not injured.
However, the newspaper reported the militant leaders were killed in a pre-dawn attack by JTF forces in Kano.
Two other men arrested were suspected to be high-profile commanders of Boko Haram.
A BBC report said a member of the militant Islamist group was killed in the clash. The JTF had not yet identified the deceased, but a source whose name was not mentioned said it was Qaqa, who was a Boko Haram spokesman.
Voice of America said a vehicle carrying three men was intercepted by Nigerian troops following a tip.