The US-led coalition fighting ISIS is verifying whether an air strike in Syria killed French militant Fabien Clain – the voice on a recording claiming the November 2015 attacks on Paris in which 129 people died.
Clain became known as the French voice of ISIS after he read out the six-minute statement.
In the recording, a man believed to be his brother gave a rallying cry to music for Muslims to fight the infidels "without ever capitulating".
"Checks are being made," a French source said. A US official in Washington said the coalition believed Clain was killed in a strike on Wednesday.
France Info radio and BFM TV reported earlier that Clain had been killed and his brother Jean-Michel seriously wounded after a coalition strike in Baghouz, the final pocket held by the militants in north-eastern Syria.
French authorities estimate that about 100 French ISIS members may still be fighting in Baghouz and say dozens are being held by Kurdish-led groups in northern Syria.
"During coalition operations to regain ISIS's last bastion, it is possible indeed that Fabien Clain was killed," French Defence Minister Florence Parly said on her Twitter account.
Ms Parly said the French people would be relieved if the information were confirmed.
Clain was jailed in the past for recruiting fighters and was believed by French authorities to have fled to Syria in 2015.
They say he played a bigger role in the November 13 attacks, the worst in France since the Second World War, than just recording the claim.
A squad of gunmen and suicide bombers killed 129 people and injured more than 350 in the attack on entertainment venues in the French capital.
Clain converted to Islam in the late 1990s. Like his younger brother, he is believed by French police to have become radicalised in the early 2000s when he lived in the southern city of Toulouse where he had links with radical networks.
He was involved in the militant recruitment "Artigat cell", French officials have said. Members of that cell were believed to have been mentored by Salafist preacher Olivier Corel, known locally as the "white emir".
France's military and Foreign Ministry declined to comment.