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Dembele is out for two to three weeks and joins fellow striker Bobby Zamora (broken leg) in the treatment room.
With Andrew Johnson (knee) and Diomansy Kamara (foot) back in training but unavailable for selection, Eddie Johnson, Clint Dempsey or Zoltan Gera will start up front. Damien Duff (calf) is expected to return after missing the 2-0 Carling Cup defeat by Stoke in midweek.
"We are short obviously because we have lost Bobby to a long-term injury as well as Mousa," said manager Mark Hughes.
"Available to us are Clint Dempsey, Eddie Johnson and Zoltan Gera, who can play off the front.
"We have options, though ideally we'd like our full compliment of strikers to pick from."
Everton have doubts over midfielders Tim Cahill and Leon Osman for the trip to London.
Cahill is rated 50-50 after two games out with a knee problem while Osman suffered a rib injury in the midweek Carling Cup loss to Brentford.
Full-back Tony Hibbert is also unlikely to feature at Craven Cottage due to a groin strain.
Forwards Louis Saha (calf) and Victor Anichebe (knee) both remain on the sidelines while Jack Rodwell (ankle) is out long term.
Everton manager David Moyes is shocked by his side's poor start to the season but has no doubts about his players' determination to put it right.
Everton's misery after collecting just two points from their opening five Barclays Premier League fixtures was compounded as they were dumped out of the Carling Cup by League One Brentford on Tuesday.
Their form has undermined pre-season optimism founded in their superb finish to the last campaign and pressure is growing as they travel to Fulham in search of a much-needed win.
Moyes said: "We started the season with the belief, coming off two defeats in 24 last year, that we would start the season well.
"It didn't happen and that affects your confidence.
"It's disappointing because I didn't expect this. We expected to start better after the good run we had last year.
"We want to do better and nobody cares more than the players, I can see that by their attitude and the way they are training.
"Football pressure is what I do, it is what the players do. It is why we are in the business and we will get on with it."