The Toffees manager had previously stated that Champions League football was a real possibility, but has now refused to set a specific target.
"I enjoy being near the top of the league," said Moyes. "And what comes with that is people thinking how well you're doing and talking in a positive fashion.
"I enjoy that and it's something I would like to happen more often when talking about Everton near the top and how well we could do. We will shoot for the stars and see where we end up."
Everton face QPR tomorrow afternoon at Loftus Road.