Gus Poyet had been in charge of the club, but he sensationally quit after claiming the board sold one of their players without his knowledge.
"Yes, he wants to do it," Wenger told 'Corse Matin'. "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."
Henry has picked up coaching experience since retiring, acting as assistant to Belgium manager, Roberto Martinez. Martinez and Henry took Belgium to the World Cup semi-finals.
Wenger brought Henry to Arsenal from Juventus and turned him into one of the Premier League's finest ever strikers.