The centre-back has aggravated a knee injury in training and is set to miss the Europa League last-32 second-leg clash, while Fabio Borini has been ruled out for six to eight weeks
The Slovakia international was an unused substitute in Liverpool’s 5-0 win over Swansea on Sunday, and a knee injury looks set to rule him out of the second-leg tie against the Russian champions.
"Skrtel is being assessed," Rodgers said in his pre-match press conference. "I think he'll struggle with his knee, he had a knock on it and he tried to train and made it worse. It's highly unlikely he'll play."
|7/1||Liverpool are 7/1 with Coral to beat Zenit 2-0 in the Europa League on Thursday
The injury to Skrtel means Jamie Carragher and Daniel Agger are expected to continue in the centre of defence against Zenit.
Elsewhere, injury-plagued striker Fabio Borini is set to miss up to two months of the season after sustaining a dislocated shoulder in Sunday’s win against Swansea.
“By the weekend, he’ll look to have an operation and you’re then looking at six to eight weeks,” revealed Rodgers.
“It’s been a difficult season for Fabio, coming into such a big club, getting injured early on, coming back and then working hard for his moment and doing his shoulder.
“It’s been difficult for him but he’s a tough-minded young boy and he’ll get through the op well and we’ll see how he recovers.”