New York Reds Bulls striker Henry is currently training with Arsenal during the MLS off-season.
Henry enjoyed a loan spell back with the Gunners last term when the MLS campaign came to an end and Wenger is now weighing up a third spell at Arsenal for the 35-year-old.
Wenger could be in the market for striking reinforcements after admitting Marouane Chamakh could leave in January and he will also be without Gervinho for several weeks when he plays for Ivory Coast at the Africa Cup of Nations
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."
Wenger knows Henry, who has scored 228 goals for Arsenal, is influential 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 said.
"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."