According to French news outlet 'L'Equipe' Henry was unsatisfied with the guarantees made by the company set to take over the side in September.
Henry had been a priority for current owners M6, but the incoming General American Capital Partners (GACP) could not offer him the right assurances.
Henry, who assisted Roberto Martinez with Belgium at the World Cup in Russia, was serious about taking the role, and had even demanded new signings as part of the deal.
He had hoped to bring in three players before the window closed on Friday.
However, after meeting with GACP representatives and club president Stephane Martin, the talks broke down.
The Ligue 1 side have also approached former boss Laurent Blanc and Aston Villa manager Remi Garde.
Bordeaux have been forced to find a new manager after they parted with Gustavo Poyet.
Poyet was suspended from his duties after calling the owners a "disgrace" after they sold striker Gaeten Laborde to rivals Montpellier.
After quitting his job as a pundit for 'Sky Sports' Henry made it clear that he was looking to move into management.