The 35-year-old has been training at his former side's Hertfordshire base to maintain fitness following the end of the Major League Soccer season with New York Red Bulls.
Henry, who joined Barcelona in the summer of 2006, returned to Arsenal on loan last year, making four appearances and extending his club record goal tally to 228.
With Ivory Coast forward Gervinho set to be away at the African Nations Cup from mid-January and Morocco striker Marouane Chamakh expected to leave the club, Wenger is likely to consider taking the Frenchman on another short-term deal.
"Thierry has been practising with us," Wenger said. "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. He is sharp.
"I had always resisted. Last year I did it because we lost Gervinho. It was a good connection.
"This year we lose Gervinho again as they are playing in the African Cup of Nations two years in a row, so we will be confronted with a shortage particularly if Chamakh should go. I cannot stand in his way, then we will be short."
Henry, part of the Invincibles squad, made a major impact in his short time back at Arsenal last season.
Wenger added: "You know what Thierry gives you; he gives you hope, especially when he comes on, that is the most important thing.
"Thierry 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.
"I think now this team has an exceptionally good character. There are not many flashy boys. What is the most important thing is not whether you are an extrovert, but what it means to you to do well, your job, your will to win."
Arsenal overcame 10-man Tottenham 5-2 at Emirates Stadium on Saturday to give themselves a much-needed confidence boost following some indifferent displays.
One of those was in their previous home European tie, when their long unbeaten run was ended after Schalke ran out deserved 2-0 winners to take command of Group B.
Victory over Montpellier on Wednesday, coupled with defeat for Olympiacos in Germany, would send the Gunners into the last 16 with a game to spare, although top spot would then most likely be out of reach, and with it seeding for the knockout stages.
"The Schalke game, at home, puts us under pressure to deliver against Montpellier. We cannot afford to happen what happened against Schalke again," Wenger said.
"Fortunately we had a good result on Saturday and I think that will help us going into the game.
"You could see before the Tottenham match that the dynamics, the confidence was better again. Hopefully that will be a good basis to build on because you say always 'We are good, we are good' but when you don't win people say 'Maybe you are wrong'.
"Circumstances went a bit for us on Saturday, but what is important is to win the game and to build and lift the confidence."
Arsenal will be without forward Theo Walcott because of a shoulder injury, but Gervinho and defender Kieran Gibbs are in contention after their recent lay-offs.
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