Gilberto Rodriguez Léal, a 61-year old French national, was kidnapped on November 20 by armed men while travelling in western Mali near the border with Senegal and Mauritania.
The Movement for Openness and Jihad in West Africa, MUJAO, claimed responsibility for the kidnapping.
A MUJAO spokesman, Walid Abu Sarhaoui, told news agency AFP that MUJAO is ready to negotiate Legal’s release.
“We Muslims can come to an understanding on the issue of war,” he said.
The announcement came as a French-led campaign to drive out Islamist rebels in northern Mali entered its 16th day.
West African defence chiefs are meeting on Saturday in the Ivorian capital, Abidjan, to discuss ways to send more African soldiers to Mali as soon as possible.