The England international was due to return to Highbury Stadium on FA Cup third-round weekend, five and a half years after leaving the club to join Leicester in a £1m deal.
Vardy is currently struggling with a groin problem, though, which kept him out of the 3-0 win against Huddersfield Town on New Year's Day, and Puel will make a late decision on his inclusion.
"We will see. If he cannot be 100%, we will not risk him," Puel told reporters. "He is not training with the team. He is just doing some exercises in the gym. For the moment, it is not good for him."