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.
"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."