The forward missed the 3-0 win over Zorya Luhansk on Thursday night because of a calf problem as he watched the Europa League win from the stands at the King Power.
Vardy now faces a race against time in a bid to be fit to face the Gunners with the injury disrupting what has been a terrific start to the season.
But speaking to BT Sport after the game, Rodgers says he will monitor the forward closely.
“We'll see how he is over the next couple of days and hopefully he can be available for the weekend," he said.
“But we'll see about that in the next 48 hours.
“It's important to get all the players back not just Jamie. We've got a number of players, very important players, that are out.
“But at the front end of the pitch, of course, offers a threat with his speed, his movement and how clinical he is."