French jihadist Fabien Clain has made a statement alleging that the Paris attacks on the 201
Security sources told the French media that an air strike killed Clain in Baghuz on Wednesday, the last bag owned by IS.
US-led coalition battles ISIS for trying to review reports.
Clain became known as the French Voice following the 2015 attacks, in which 130 people died.
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What is known about the air raid on Wednesday?
It was conducted overnight by the US-led coalition, sources of security reported to the French media.
They said Clain's brother and fellow scholar Jihadist Jean-Michel was seriously injured in the strike.
French Defense Minister Florence Parly tweeted later (in French), that Fabien Clain was "possibly" killed.
Fabien Clain is believed to have come to Syria in 2015.
Almost 2,000 French citizens have been fighting for IS in Syria and Iraq since 2014, the French government believes.
How close is the capture of Baghuz?
It is estimated that about 300 IS fighters are trapped in and around the village on the border with Iraq.
Civilians have been evacuated from the village in recent days.
The US-backed Syrian Democratic Army (SDF) has said they are waiting for their withdrawal before launching an offensive against "internally entrenched" militants.
The removed ones are screened and put into storage, according to the SDF.
The case of Baghuz is significant – but the experts have warned against the ideological move of the group.
At its peak five years ago, IS was a controlled area of 88,000 km² (34,000 km²) from western Syria to eastern Iraq.