West Ham are without a win in five, with Allardyce beginning to come under pressure for his decision to play without a recognised forward.
Jol's side have slumped to four miserable defeats in a row, and the input of new head coach Rene Meulensteen did not have an immediate effect as the Cottagers went down 2-1 at home to Swansea City.
The hosts will remain without Andy Carroll and Winston Reid, the latter being a long-term absentee, but there could be space for Mladen Petric to make an appearance against his old club.
For Fulham, captain Brede Hangeland is unlikely to return to fitness, but Ashkan Dejagah could be tried on the right flank to provide width.
West Ham: WLDDLL
Possible starting lineups
West Ham: Jaaskelainen; Demel, Collins, Tomkins, O'Brien; Collison, Noble; Nolan, Morrison, Downing; Petric
Fulham: Stekelenburg; Zverotic, Hughes, Amorebieta, Richardson; Boateng; Dejagah, Parker, Kasami; Berbatov; Bent
Sports Mole says: 2-1