The 35-year-old New York Red Bulls striker is back training in north London during the MLS off-season, and after enjoying a brief stint back with the Gunners last campaign, the Frenchman might be tempted into a third spell in 2012/13.
Wenger has hinted he could be in the market for striker reinforcements in January, after admitting that Marouane Chamakh may leave the Emirates Stadium, while Arsenal will also be without the services of Gervinho for several weeks, when he heads off on Africa Cup of Nations duty in the New Year.
Asked whether he had considered making another offer to Henry, Wenger said: "He has been practising with us. Three times. Will I sign him again in January? I don't know - I don't rule it out. I don't know if he would be interested.
"This year we will lose Gervinho to the Africa Cup of Nations again, so we will be short - particularly if Chamakh goes."
With 228 goals for Arsenal, Henry holds a hero's status amongst Arsenal fans and players, and Wenger knows that securing his signature - even on a short-term basis - could be a huge confidence boost, because of his influence both on and off the pitch.
"You know what he gives you. He gives you hope, especially when he comes on. That is the most important thing," he added.
"He is a communicator. An extrovert. Very intelligent. He can only give good advice to players because he was in their position when he arrived here."
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