The Blue half of Merseyside haven't experienced derby success at Anfield during Moyes 10-year tenure, their last away-day triumph coming in 1999.
The Scot celebrated 10 years in charge of the Toffees this week and is hoping to mark the milestone with his first away victory in a Merseyside derby.
The Blues have added incentive as a win would see them leapfrog their rivals into seventh in the Premier League.
Asked if he would be happy simply not to lose the game, Moyes replied: "Over the years, I think it would have been a great result for any team to go and do that, because Anfield has been a hard place to go.
"Liverpool have got really good support and a good team. It has never changed.
"We will go to Anfield and try to win, and then if you can't do that, the next thing you want to do is try to get a draw."
Everton go into the match unbeaten in nine matches in all competitions, a run which has included victories over Chelsea, Manchester City and Tottenham - albeit all at Goodison Park.
But, whilst Kenny Dalglish's Reds have won just once in eight league games, Moyes believes form goes out of the window on such an occasion.
He added: "A lot of the years I have gone into the game and Liverpool have been the form team, and folk have said: 'Who knows in derbies'.
"You never do know."
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