Van Persie's long-term future in North London appears uncertain after he confirmed earlier this month that he will not be signing an extension to his contract, which expires next year.
Manchester City, Manchester United and Juventus are all keen on the striker, but no clubs have yet matched Arsenal's valuation of their captain.
Henry left Arsenal for Barcelona in 2007, before returning for a loan spell earlier this year, while the likes of Cesc Fabregas and Samir Nasri have also been high-profile departures from the club in recent seasons.
If the Netherlands international follows the lead of several of his former colleagues, Henry remains confident that the Gunners can still challenge for honours.
"We hope it stays, and that's the way it is," Henry told Sky Sports News. "I don't know exactly what is happening but as an Arsenal fan I want him to stay.
"He is still an Arsenal player and the boss has to deal with it."
When asked about Van Persie stating he will not sign a new contract, Henry replied: "I've got nothing to say about that, you will not get me to be one of the guys talking about the club and the player.
"I just want Arsenal to do well. Robin will do what he will do and we'll see.
"When I left, everybody cried, but then the year after they went on a run of being eight points ahead. Everyone comes and goes."