Henry, 41, has been working as an assistant to Belgium head coach Roberto Martinez over the last two years and has been lauded for his impact with the 2018 World Cup semi-finalists.
After quitting his role as a Sky Sports pundit to pursue a senior management role the Les Blues all-time record scorer was tipped to replace Gus Poyet at Bordeaux.
He had reportedly been negotiating with the club and their soon-to-be American owners in recent days.
However, according to L'Equipe, United States investment fund GACP, which is set to complete a buyout of Bordeaux's owners was left unimpressed by his excessive demands.
L'Equipe claims his €200k (R3.3m) monthly salary, the logistical demands made for his family and the commission of his agent, Darren Dein, were major stumbling blocks.
"The conditions demanded by his agent are off the scale given he doesn't have any experience," a Bordeaux official told L'Equipe.
"We didn't have to face up to those sorts of demands for Laurent Blanc when he started his career."