Former Chelsea boss Antonio Conte is a candidate for the Bordeaux job.
Arsenal legend Thierry Henry has been in talks for the post since the axing of Gus Poyet at the start of the season. However, French sources say Henry has rejected the offer over the weekend.
Sud-Ouest says Bordeaux are now seeking alternatives and Conte is now under consideration. Another former Blues manager, Claudio Ranieri, is also being sounded out.
Talks have already commenced with the minders of both managers.