Wenger has come in for criticism at times over recent seasons, with Wednesday's 3-1 home defeat to Monaco in the UEFA Champions League last 16 bringing the Frenchman's future under the spotlight once again.
Arsenal legend Henry is currently working in the British media, having called time on his playing career with the New York Red Bulls last year.
"The thing that I will say is, I don't know what Arsene wants to do and how long he will stay, I just want to be equipped to be in the position one day maybe to be a manager," he told The Jonathan Ross Show.
"Being the manager of Arsenal Football Club will be a dream, but let's all be honest, I need to learn first, that's the most important thing.
"It's not because you know the game that you can teach it and I just want to learn."
Asked what his response would be if offered the job by Wenger, Henry - who is working towards his coaching badges - replied: "I can't say no to Arsenal, so I would say yes."
Henry has been coaching youngsters at Arsenal in recent weeks.
‘It was without a doubt one of the most important matches that I played in my career. It wasn’t just Champions League football – it was a whole club at stake’: Ex-Chelsea star opens up on key game which changed the Blues' fortunes forever
'I was Arsenal captain and really enjoyed it, but when Man City come calling, you have to listen': England international reveals reason for swapping London with Manchester
