James Tomkins was expected to miss the game after suffering a groin injury during last weekend's goalless draw at Millwall but Sam Allardyce is hopeful the Hammers centre-half could yet be fit.
Winston Reid came on as a substitute at The Den and will start alongside Abdoulaye Faye, who will be making his full home debut, if Tomkins does miss out.
Allardyce is otherwise expected to name an unchanged side, with Carlton Cole as the lone frontman and recent signing Sam Baldock on the bench.
Fellow striker Frederic Piquionne is still suspended, midfielder Papa Bouba Diop is building up his fitness, right-back Guy Demel is recovering from a hamstring problem and winger Gary O'Neil (ankle) is still out.
Gabriel Zakuani should retain his place in the Posh side.
The Congolese defender has been nursing a toe injury in recent weeks and is receiving injections in a bid to keep him available for the trip to east London.
Long-term absentee David Hibbert (knee) aside, manager Darren Ferguson has a full complement of players to choose from.
Striker Emile Sinclair will hope to keep his place in the starting line up after marking his full debut with a goal in the 2-1 home win over Burnley last weekend.
Ferguson has defenders Scott Wootton and Ben Gordon, midfielders Tommy Rowe and Daniel Kearns and striker Paul Taylor available should he wish to make changes.
Striker Nicky Ajose has joined Scunthorpe on loan until the start of January in order to build up his match fitness after recovering from the hamstring injury he sustained on the opening day of the season.