Bordeaux are seeking a new coach after the sacking of former Brighton manager Gus Poyet. The Uruguayan was shown the door after attacking the club's owners in public.
Henry has immediately been named favourite for the post.
Also under consideration are Jurgen Klinsmann, Laurent Blanc and Rémi Garde, though Henry remains the overwhelming favourite for the job.
Henry announced he intended to launch a career in club management after leaving Belgium's setup following the World Cup.