Gibson clear to face Wigan
Everton midfielder Darron Gibson will be eligible to play against Wigan on Boxing Day as his appeal against his red card at West Ham cannot be heard until later in the week.
The Republic of Ireland international will not serve a suspension - if any - until the Football Association have had time to consider his case.
"We think there's a real reason to ask the FA to re-look at it," said Moyes, who believes Wednesday's opponents have not had the credit they deserve despite being in the bottom three.
"Roberto Martinez has done a really good job there, he has a good technical side and they are a test for all teams.
"Folk think their league position is a guide but I don't think so, I think they have played some good football and we will have to do all the right things.
"You always want to come out of the Christmas period being no worse but if you can do better than your league position was when you went into it then that is great.
"It is an important time and once you come through this you are into January and you know the finishing line is in the distance."
Gibson's fellow midfielder Marouane Fellaini serves the second of a three-match ban while Seamus Coleman, Tony Hibbert and Kevin Mirallas have all been kept out recently by injury.
Wigan captain Gary Caldwell could make his return to action at Goodison Park.
Caldwell, recently sidelined by a hamstring problem, was back in the squad for Saturday's 1-0 home defeat to Arsenal as an unused substitute and will be assessed by manager Roberto Martinez ahead of the short trip to Merseyside.
Fellow centre-back Ivan Ramis, who has also been nursing a hamstring complaint, has a chance of featuring as well, but midfielder James McCarthy (ankle) is a doubt.
Antolin Alcaraz (groin), Adrian Lopez (hamstring), Albert Crusat (knee), Ryo Miyaichi (ankle) and Ben Watson (broken leg) remain on the Latics' lengthy casualty list.
Martinez believes Everton "tick every box" but is confident his team can provide more than a match for them.
Asked if he thought the Toffees would be able to sustain their top-four push, Martinez said: "Yes, because of the experience they have got and because of the way they have started the season.
"We all know that Everton traditionally start seasons a little bit slowly and then finish at a very good level.
"But we can speak from our own experience. It will be our second game against Everton and in the first one, it was the best Everton side we have faced.
"This Everton side tick every box. They have been able to get consistently good results in this league and that allows you to be fighting for the top four positions.
"At Goodison Park they are unbeaten and it is one of the hardest places to visit in the Premier League.
"We are well aware of all that, but we feel we can match Everton on our day."