Wenger made the comments in an interview with Corse Matin (h/t AS):
"Yes, he wants to do it, he is intelligent and he has the qualities.
"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."
Per the report, Bordeaux suspended current coach Gus Poyet after he hit out at the club over the sale of Gaetan Laborde to Montpellier.
While Poyet has officially been suspended, the French media are convinced he no longer has a future with Les Girondins and are already reporting on his sacking. According to the likes of Goal France and L'Equipe (h/t Get French Football News), Laurent Blanc, Remi Garde, Jurgen Klinsmann and Michael Laudrup are all possible replacements.
All outlets appear to name Henry as the favourite, however. The Arsenal legend is coming off a big summer, working as an assistant alongside Roberto Martinez with Belgium. The Red Devils finished third at the FIFA World Cup, their best-ever result.
The other candidates all have more experience than Henry, but it's the 41 year old who presents the most exciting option because of his relative inexperience. He's only had success as an assistant, and perhaps that will carry over when he takes the step up.
Les Girondins finished the 2017-18 Ligue 1 campaign in sixth place and traditionally slot in behind France's elite clubs, including Paris Saint-Germain, AS Monaco, Lyon and Marseille. They've gone nearly a decade without a Ligue 1 title and haven't won the Coupe de France in years, either, so the expectations wouldn't be very high if he took over at this stage.
Poyet could still be reinstated, but given the nature of his comments regarding the club, that seems unlikely at this point, via GFFN:
Bordeaux will take on Belgian side Gent in an all-important UEFA Europa League play-off series, with the first of two matches on Thursday. They'll face Monaco in Ligue 1 on Sunday.