Victory over Liverpool on Sunday will effectively hand Everton a top-six position when the Premier League season ends in two weeks' time, but Moyes has targeted finishing as high as they possibly can.
The Scot told reporters: "You want to finish above every team - I wanted to finish above Manchester United and Manchester City this season
"Do I want to finish above Liverpool? Of course I do. But it can't be our sole objective, and I would be surprised if it was Liverpool's to finish above us.
"In terms of our target at the moment, we are looking to see if we can catch Tottenham or one of the other teams above us."
Everton travel to Liverpool on Sunday with Moyes yet to win a Merseyside derby at Anfield.