The Frenchman is a step closer to making an amazing comeback to the Premier League after the North London club offered him a short-term deal until March when he returns to the New York Red Bulls.
That has led to speculation over what shirt number he would be handed at the Emirates, with his legendary No.14 currently taken by Theo Walcott.
According to The Daily Mail, the 34-year-old will be handed the No.12 shirt during his two-month stint with the Gunners - the number he donned for France.
Meanwhile, Wenger has warned Arsenal fans not to expect the Henry of 10 years ago.
"You can never take away from people what they have done, that will remain forever. Nobody expects him to be what he was 10 years ago, we just want him to help out.
"I think it is just credit to him to be wanting to be helpful to a club that has given him so much. Therefore I feel there is no special pressure to be the player he was before.
"You cannot put too much pressure on him. He is here to help out, not to suddenly be the leader, the main player in the squad, and I respect his desire to help us get through a period where we lose two strikers.
"He and I are conscious that he is 34 years old, but he has not lost his class or his brain. That will be just enough for us."
Should Henry sign, he could feature as early as Monday against Fulham.