The Frenchman has served as assistant coach to Belgium national team boss Roberto Martinez since 2016, while the Spaniard has performed the same role under Manchester City manager Pep Guardiola.
"I don't want to influence that publicly, because for me I believe it is important that they make their choice in an objective way", he said, "and after, once they make a decision, I will support them".
Even though former Arsenal midfielder Arteta has emerged as the favourite to replace Arsene Wenger, the fact that Henry has been approached suggests there could yet be a twist.
"I am going to give myself until June 14, the day the World Cup begins, to decide". "Because I want my club to continue to do well and continue to play at the top. As I said in my speech on the pitch after the Burnley game, I'm a fan above all".
He also said it would be "difficult" to manage another team in England because of his time at Arsenal.
"At the moment if I want to continue to work, I think I have to move out of the country, because my gut feeling at the moment is that I would feel I would betray my club by staying in England".
"But they didn't ask me, so that takes the weight away from me..." I think people are too hard on them, too demanding. I get bored. I need to be doing something.
And it seems Leno will be joined by a new defence in front of him, with the Daily Mirror reporting that Arsenal are close to finalising summer swoops for Sokratis Papastathopoulos from Borussia Dortmund, West Brom's Jonny Evans and Caglar Soyuncu of Freiburg. I have lived and breathed football all these years and it's a passion.