The Toffees welcome the title-chasers to Goodison Park on Tuesday evening and their boss hopes Roberto Mancini's side will not be on top form and that his team are at their best
The Toffees have lost just once in the last 13 Premier League clashes between the sides at Goodison Park but, considering City's big-spending and rise to the Premier League summit, that means very little.
City haven't been firing on all cylinders recently though, and Moyes is hoping his side can take advantage of the Citizens' current blip.
Moyes said: "I think all sides will go through periods of difficulty during a season and Man City are probably just in a bit of that at the moment.
"They have lost a couple of boys to the African Nations Cup and there have been a couple of disciplinary things which they see haven't gone their way. It can sometimes just upset the rhythm at the club.
"Let's hope it is upset because we are going to have to hopefully catch them on an off night and us play very well.
"Over the years we have always had quite a good record against Manchester City."
Moyes was also full of praise for the improvements that Mancini has made to his side, pointing out that City are far improved even from last season.
"The difference is they have improved, and they have improved from last season, you can see that from their league position" continued Moyes.
"Their players have got better, there is more belief, more understanding playing alongside each other.
"We are coming up against a far better, far greater Manchester City side than even we played last year."