The Frenchman returned to the club where he scored 226 goals over an eight-year period on a short-team deal last season, famously netting the winner in an FA Cup clash with Leeds.
And Wenger has admitted that he has not yet ruled out a third Gunners stint for Henry, with the 35-year-old's current club, the New York Red Bulls, out of action during the MLS off-season.
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"He's still coming today to practice with us. We are very close, but at the moment I think he has had a second spell at the club that was very successful. You have to be cautious that it's not one time too many."