Alabama-born Omar Hammami -- better known as Al-Amriki or "the American" -- was one of the most prominent foreigners fighting in Somalia, and the US State Department had offered a USD 5 million bounty for his capture.
"There was a gun battle between Amriki and his men and other fighters, the reports are that Amriki is among those killed," said Moalim Ali, a resident in Bardhere, a small settlement in southern Somalia.
Two other extremists were also killed in the battle, including one other foreigner.
"Amriki and two other fighters, one of them foreigner, have been killed near Bardhere," said Mohamed Wardhere, another resident.
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There was no immediate response from the Shebab.
Hammami, 29, moved to Somalia in 2006 and began to work for Shebab recruiting young trainees through his English-language rap songs and videos.
Jerky videos showed him enthusiastically promoting the Shebab's battle to overthrow the internationally backed government, but he later fell out with top Shebab leader Ahmed Abdi Godane, for whom the US has offered USD 7 million.
Fazul is thought to have planned the 1998 truck bombings of the US embassies in Nairobi and Dar es Salaam, and had a USD 5 million bounty on his head.
In turn, the Shebab accused Amriki of "spreading discord and disunity" and a "narcissistic pursuit of fame".
He had previously warned of assassination attempts against him, and posted forlorn photographs on his Twitter account posing with automatic rifles, his lank hair held back by a checked headscarf.
The death of Hammami makes him the latest extremist to be killed by infighting within the group, and will bolster Godane's control.
Abdi Aynte, head of the Somali think-tank the Heritage Institute for Policy Studies, said that if confirmed, Hammami's death would mean the "anti-Godane alliance is almost neutralised".
In June, Godane's men killed two co-founders of the group, one with one with a USD 5 million US bounty, Ibrahim Haji Jama Mead, better known by his nickname Al-Afghani -- "the Afghan".