Parker has a virus while Kieron Dyer (hamstring) and Valon Behrami (hip) will also be assessed.
Enlarge Crucial game: Parker (left) will be desperate to play in a match that if West Ham lose, could see them seven points adrift of safety
Young forward Zavon Hines (knee) is fit again, but Mark Noble (hip) is set for another spell on the sidelines having only just returned from an appendix operation.
Manuel Da Costa (ankle), Thomas Hitzlsperger (thigh), Jack Collison (knee) and Junior Stanislas (groin) remain out.
Team (from): Green, Gabbidon, Jacobsen, Upson, Ilunga, Tomkins, Kovac, Boa Morte, Piquionne, Cole, McCarthy, Obinna, Spector, Stech, Reid, Nouble, Parker, Dyer, Behrami, Hines.
CLICK HERE FOR THE WEEKEND TEAM NEWS IN THE BARCLAYS PREMIER LEAGUE Explore more:People: Jack Collison, Kieron Dyer, Thomas Hitzlsperger