Bordeaux suspended Gustavo Poyet after the head coach described the decision to sell Gaetan Laborde to Montpellier as "a disgrace".
Henry, part of Belgium's coaching staff at the World Cup, was linked with taking over at Championship club Aston Villa ahead of the 2018-2019 season before their new owners opted to retain manager Steve Bruce.
Arsenal's record goalscorer also reportedly held talks with Egypt over the prospect of becoming its next manager, according to an agent involved in the discussions, although Henry has since dismissed the claim.
But former Arsenal boss Wenger says Henry, who has quit his role as a television pundit to focus on his managerial career, is keen on replacing Poyet at Bordeaux, who are in the Europa League's play-off round.
"Yes, he wants to do it, he is intelligent and he has the qualities," Wenger said.
"The existential question that we always ask ourselves is whether we are ready to sacrifice our life for the coaching profession.
"Being passionate is selfish work. When you are passionate, you steal your time from those whom you love and to whom you could have given much more."
As for his own career, Wenger has yet to decide whether he will seek another coaching post after leaving Arsenal at the end of the 2017-2018 campaign.
"I decided not to decide," the Frenchman said. "I was intoxicated for such a long time that I promised myself not to make any decisions before September.
"When you have been as busy as I have been, you always fear a little emptiness. But I quickly organised myself in this new stage of my life, I do a lot of sport, here I eat with my friends.
"I talk a lot too, I can sit for hours contemplating the horizon, I read every day."