"There is a very strong probability that he is dead.... This requires verification on the ground, which is not simple," said a Western security source, who asked not be identified.
A senior Somali security official echoed the comment.
"We believe that the Shebab leader is dead, though we don't have his body. Most probably he is dead," said the official, who also spoke on condition of anonymity.
He said he believed the Shebab were now "talking about a successor" to Ahmed Abdi Godane after late Monday's air strike.
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A senior Somali security official also said Ahmed Abdi Godane was "most probably" killed.
Contacted by AFP, Shebab officials maintained their position of refusing to confirm or deny the reports.
"We don't want to comment on this American propaganda that they have killed our leader," a senior Shebab official said.
Washington has carried out a series of drone missile strikes in the past, including attacks reportedly targeting Godane -- listed by the US State Department as one of the world's eight top terror fugitives.
Godane, 37, who reportedly trained in Afghanistan with the Taliban, took over the leadership of the Shebab in 2008 after then chief Adan Hashi Ayro was killed by a US missile strike.
The Shebab are fighting to topple Somalia's internationally-backed government, and regularly launch attacks against state targets, as well as in neighbouring countries that contribute to an African Union force.