"I think it's very likely true based on the sources I am seeing," said J.M. Berger, who runs the website Intelwire.com.
The rebels did not immediately present proof of Hammami's death.
A member of al-Shabab who gave his name as Sheik Abu Mohammed told The Associated Press that Hammami was killed in an ambush in Somalia's southern Bay region. Some of Mohammed's associates carried out the killing, he said. Two other fighters with Hammami, including a Briton of Somali descent, were also killed, he said.
Along with Adam Gadahn in Pakistan — a former Osama bin Laden spokesman — the 29-year-old Hammami is one of the two most notorious Americans in jihad groups. He grew up in Daphne, a community of 20,000 outside Mobile, the son of a Christian mother and a Syrian-born Muslim father.
His YouTube videos that featured him rapping and his presence on Twitter made him one of the most recognizable and studied U.S. foreign fighters. The U.S. put Hammami on its Most Wanted terrorist list in March and offered a $5 million reward for information leading to his capture.
U.S. prosecutors had charged Hammami with providing material support to terrorists.
In Alabama, Husam Omar, vice president of the Islamic Society in the city of Mobile, a mosque Hammami once attended, said he had not heard of the reports of his death.
"I'm shocked," Omar said, declining further comment.
Hammami moved from Alabama to Somalia and joined al-Shabab in about 2006. He fought alongside al-Shabab for years until they had a falling out amid signs of increasing tension between Somali and foreign fighters in the group. He first expressed fear for his life in a web video in March 2012 that publicized his rift with al-Shabab.
The first serious attempt on his life was made in April.
"Just been shot in neck by shabab assassin. not critical yet," Hammami tweeted after the April attack. He later wrote on Twitter that the leader of al-Shabab was sending in forces from multiple directions. "we are few but we might get back up. abu zubayr has gone mad. he's starting a civil war," Hammami posted.
Hammami accused al-Shabab's leaders of living extravagant lifestyles with the taxes fighters collect from Somali residents. Another Hammami grievance is that the Somali militant leaders sideline foreign militants inside al-Shabab and are concerned only about fighting in Somalia, not globally.
The leader of al-Shabab, Mukhtar Abu Zubeyr, is also known as Godane.
Berger said that Hammami has been "a thorn in the side of al-Shabab" for more than two years and "one of the few surviving dissenters after Godane's bloody purge over the summer."
Before the falling out, Hammami made frequent appearances in al-Shabab combat videos, and in 2011 he released two rap songs, "Send Me a Cruise (missile)" and "Make Jihad With Me."