The 32-year-old injured his right Achilles tendon during a Champions League match in October 2016 and has since been forced to have surgery nine times in an attempt to correct the problem.
In an interview earlier this month, the Spaniard admitted that his foot almost had to be amputated due to an infection, prompting fears that his playing career may already be over.
"It is the worst injury I've known," Wenger told reporters today when asked about Cazorla's condition. "It's gone from worse to worse. I know how much Santi loves to play football.
"I wish [he returns in January]. He tries to practice. I hope he comes back in January."
Asked if there was a possibility Cazorla could never play again, he responded: "I hope that you are wrong."
Cazorla has been with Arsenal since 2012, scoring 25 goals in 129 Premier League appearances and winning two FA Cups.