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.