The defender has been sidelined for the team's last two games after picking up a knee injury during last month's 3-1 defeat to Manchester City.
Despite the Slovakia international's recent return to training, Rodgers expects the centre-back to sit out tomorrow night's match at Anfield.
"Martin has worked very hard. He joined the group yesterday, so he is working well," he is quoted as saying by Sky Sports News. "It's probably too early for this game but after a good week's training he should be ready for West Ham."
Liverpool continue their Premier League campaign on Saturday when they make the trip to Upton Park.