Shishani, whose real name is Tarkhan Batirashvili, was wounded this month and died on Monday outside the ISIL's main stronghold of Raqqa, in Syria, the sources told the AP news agency.
A US military spokesman confirmed the reports, al-Jazeera said in another report.
A US air strike targeted Shishani on March 4 near Eastern Syrian town of Shaddadeh, Peter Cook, the Pentagon press secretary, said last week.
Rami Abdurrahman, head of the Britain-based Syrian Observatory for Human Rights, said after Shishani was wounded, ISIL "brought a number of doctors to treat him, but they were not able to".
The spokesman for the US-led coalition, Army Colonel Steve Warren, said on Tuesday the coalition was able to "assess that he is dead" and that it "got the word Monday morning;" FNA reported.
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