The Nigerian security source, who could not be named, said the man killed had been identified as Abu Qaqa, whose name frequently appears in pronouncements on behalf of the sect from its northeastern base.
He said that one of the two arrested was suspected to be a top Boko Haram commander, Reuters reports.
A spokesman for the military and police joint task force in Kano, Lieutenant Ikedichi, said checks were being made to determine the identities of the three men.
Nigerian authorities in March claimed to have captured Abu Qaqa, but the man turned out to be another of the sect's members. Verifying his death is complicated by the fact that the name is probably a pseudonym.
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