The Foxes are facing a key quarter-final clash in Europe on Thursday, but will have to do without their main goalscorer.
Vardy is still not fully fit from a knee ligament injury, which is causing him pain.
"He's not available," Rodgers said in a press conference.
"It's hard to put a timeline on it. He can still feel pain in the knee. It's just when he's striking the ball there is an issue, so we have to try to get to the bottom of that.
"I just had a quick chat with Jamie, he'd been outside and he'd been running in straight lines, but when he was opening up the MCL, when he was striking the ball, he had a little bit of pain in that.
"I'll have to speak with the medical team to see where that's at. It doesn't sound as if he's too close to being back."