Verdon was one of two French hostages kidnapped in the northern Mali town of Hombori in November 2011. The French foreign ministry declined to comment.
Another 14 French hostages are detained in Western African, including seven believed to be held in the Sahel by al Qaeda in the Islamic Maghreb (AQIM) and its affiliates.
One of AQIM's leaders, Mokhtar Belmokhtar, had pledged revenge after France launched a campaign in January to dislodge the group and other Islamist militants who had hijacked a Tuareg rebellion in the Sahel nation and seized the northern half of the country.
After driving them from the main cities of Gao, Timbuktu and Kidal in a swift, nine-week assault, some 1,600 French and Chadian troops began searching for Islamist rebels in their pocket hideouts in the mountainous region of northern Mali.
The AQIM commander described Verdon as a French spy. He said that French President Francois Hollande "bore the responsibility for the remaining hostages".
When asked by the agency whether Belmokhtar had been killed, he neither denied nor confirmed it. There have been conflicting reports on whether Belmokhtar was killed in the French military campaign against the rebels.