Moyes, who has been in charge at Goodison Park since 2002, has yet to record a victory at Old Trafford, with their last win there coming over 20 years ago.
However, they did draw 4-4 at United last season and beat the Red Devils 1-0 on Merseyside in the first game of this league campaign, during which they have only lost three games.
"Someone told me it was 1992 when we last won at Old Trafford, so that tells you how difficult the task is," Moyes said. "But we have been quite good this year in that we have not lost many games and always been in there.
"We won earlier in the season against Manchester United and we drew there at the end of last season, so we will go there probably in a better frame of mind and with a little bit more confidence than at any other time since I arrived here.
"We will go there and try to get a positive result."
The Scot is under no illusions as to the size of the challenge facing his side as they face a United team who are 20 points better off than his own and currently lead the Premier League by nine points.
"I have great respect for the manager and the way they run their club at Manchester United," Moyes said. "I have to say, we think we are having a great season, and they are 20 points ahead of us right now.
"I'm shaking my head in disbelief. We have not played too badly in many games this season. So it says a lot about Manchester United that they have 20 points more than us - and about the level you have to get to if you are going to really have any chance of competing to win the league."
Moyes is hoping the fact United face Real Madrid in the last 16 of the Champions League on Wednesday may prove a factor for Saturday's game, adding: "It will be a hard job for us, but with a bit of luck, maybe they might have Madrid on their mind for Wednesday night and rest a few players."
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