Palace, who sit rock-bottom of the Premier League after losing nine of their first 10 matches, are already six points adrift of safety.
Still searching for a new manager after Ian Holloway's departure, Palace have scored just six league goals – no side has netted fewer in the Premier League – and they are already facing a battle against relegation.
Everton boss Roberto Martinez, meanwhile, has made a bright start to life on Merseyside, guiding the club to seventh in the table, just a point behind second-placed Chelsea.
And although he is not getting complacent ahead of the trip to Palace, Everton will make the journey as heavy favourites to post their sixth league win of the campaign.
"You can never take any game lightly, Crystal Palace have been unfortunate in terms of results, they have been in games," Martinez said on Thursday.
"We will have to be at our best, really strong. Palace will be looking at their home games to achieve what they want to do. We have to understand what we have to do (to win) and be at our best.
"Every game away from home is complicated, for one reason or another you have got a situation to resolve. Unless we are at our best this team (Palace) can click at any time, we have to be prepared for that.
"I feel they are very close, they have been very unfortunate, and had a snowball effect in negative results, but they are much better than their points in the table."
Palace's only win of the Premier League season came against fellow strugglers Sunderland, and they have several injury concerns to contend with.
Caretaker manager Keith Millen – who has said that he expects Saturday to be his last match in charge of the club – will be without defenders Paddy McCarthy (groin) and Jack Hunt (ankle), while striker Glenn Murray (knee) and midfielder Jonathan Williams (ankle) will also miss out.
Adlene Guedioura is a fresh injury absentee, with the Algeria international expected to miss at least six weeks with a punctured lung and two broken ribs suffered against West Brom.
Everton also have injury concerns, with Arouna Kone (knee) a long-term absentee, joining former Wigan team-mate Antolin Alcaraz (groin) and midfielder Darron Gibson (knee) on the sidelines.
There is better news on Chelsea loanee Romelu Lukaku, who recovered from a thigh problem to feature in training this week. The Belgian has scored five goals in six league appearances so far this campaign.
Everton's only loss of the Premier League season came on the road at Manchester City last month, but they have bounced back strongly since then and could move into the top four with a victory.
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