The 35-year-old won two Premier League titles and three FA Cups during his eight years in North London, in which time he became the Gunners' record goalscorer.
Henry has two years left on his contract with MLS outfit New York Red Bulls, but said that he will remain in the game when his career is over.
"All I know is that I will be involved in the game for sure and hopefully be involved with Arsenal, because that is the heart talking there, that's the team that I support," the Daily Mail quotes the Frenchman as saying.
"In any type or shape, if I can go back to the club I would love to do it, but it's not up to me.
"That would be a desire, more a desire than something that can be officialised, I still have two years playing and then I will see. But I would definitely love to be back with Arsenal."
Henry scored twice during a short loan spell at the Emirates Stadium last season.