The in-form midfielder is suffering with a chest infection and will need a late fitness check as the Hammers look for their first win at Anfield in 47 years.
Influential: Parker would be a huge loss for the Hammers
Julien Faubert returns to the squad after suspension but Valon Behrami (hip) is still a doubt and Manuel Da Costa (ankle), Thomas Hitzlsperger (thigh) and Jack Collison (knee) are ruled out.
Young forwards Zavon Hines (knee) and Junior Stanislas (groin) are back in training but will not be risked this weekend.
Team (from): Green, Jacobsen, Upson, Ilunga, Gabbidon, Tomkins, Ben Haim, Reid, Faubert, Spector, Behrami, Barrera, Parker, Kovac, Obinna, Cole, Piquionne, McCarthy, Boa Morte, Stech.
CLICK HERE FOR THE WEEKEND TEAM NEWS IN THE BARCLAYS PREMIER LEAGUE Explore more:People: Jack Collison, Thomas Hitzlsperger, Ben Haim Places: Liverpool