The Gunners have suffered in recent years through player sales, and have gone seven seasons without a trophy, but Giroud, who is not panicking about the dip in form, insists that Wenger is owed the time to arrest the slide.
"If Arsenal are where they are, if they are known around the world, it's thanks to [Wenger]," Giroud told RMC.
"There are no worries. Everyone owes him a lot of faith. He's the man for the situation."
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Giroud insists that he does not know anything about that aspect of Henry's stay with the club, but says that he is a great player and a potential move could be "good for everyone".
He continued: "Henry is training with us. He's training with the group during the close season. I'm not going to make myself heard on the subject - it's not me who does the recruitment for the team.
"Henry is a great player and if he can bring something with him, then it's good for everyone. He has been good. We'll see how it goes. I'm not aware of all this."