Skrtel has suffered a slight knock on his knee and is unlikely to play when the Reds host the Russian side on Thursday night, when they must overturn a 2-0 first-leg deficit to book a place in the last 16 of the competition.
"He is being assessed but I think he'll struggle," said Rodgers.
"He got a little knock on his knee a few days ago and tried to train on it but made it worse. So it's highly unlikely that he will play."
Rodgers has also given the latest update on Fabio Borini after he suffered a serious shoulder injury during Liverpool's 5-0 victory over Swansea on Sunday.
"By the weekend, he'll look to have an operation and you're then looking at six to eight weeks," added Rodgers.
"It's been a difficult season for him coming into such a big club and getting injured early on. He came back, worked hard but then injured his shoulder.
"He's a tough-minded young boy, so hopefully he'll get through the operation well and we'll see how he is.
"He'll go away, he'll recover and hopefully we'll see the best of him in the future."