Defeats last weekend have dragged both London clubs into the Premier League relegation mire, leaving their managers desperate for three points to alleviate the pressure on Saturday.
West Ham were booed off after their 3-0 defeat to Chelsea last weekend, and they have not won a home league game since their opening-day triumph against Cardiff City.
Their latest defeat was their fourth home reverse of the season and boss Sam Allardyce understands the fans' frustrations.
He said: "If they (the fans) don't see the sort of determination and passion and desire they think they should get they show their disapproval.
"It's my job to pick the players up and remind them about previous performances we've had home and away this year, make sure we get to that level and stop those fears creeping in."
West Ham were forced to start with captain Kevin Nolan up front for Saturday's game, with attacking trio Ricardo Vaz Te (shoulder), Andy Carroll (ankle) and Mladen Petric (calf) all still on the sidelines.
Romanian full-back Razvan Rat also remains out with a hamstring problem, while Winston Reid is recovering from an operation on an ankle injury.
Fulham boss Martin Jol was also on the receiving end of criticism from his own fans during the 2-1 loss at home to Swansea.
A run of four straight league defeats has consigned Jol's men to the relegation zone, leading to speculation about the 57-year old's future.
The visitors will again be without the suspended Sascha Riether, who is serving the final game of his three-match ban for stamping on Manchester United's Adnan Januzaj, while Damian Duff is a doubt with a groin injury.
Hugo Rodallega and Matthew Briggs (both groin) are both ruled out, while Brede Hangeland has been struggling with a sciatic nerve problem.
