The Toffees are currently in sixth place in the Premier League table and two points off a Champions League spot after 17 games.
Neville has been understandably thrilled with Everton’s early-season form and is hoping David Moyes’ men can mount a serious challenge for a top-four finish after Christmas.
“I think we are doing really well,” Everton captain Neville told Sky Sports. “I think next week, when we play Wigan, is the turn of the year, is the halfway point, and if we can be in fifth or fourth position, that’s where we wanted to be at the start of the season.
“That’s the goal that the manager set us, be in the top four or be in and around the top four by the time we get to Christmas.
“After Christmas, that’s where the league takes shape and we normally come good after Christmas.
“The second half of the season is where go up a couple of gears and I still think there is more to come from the team.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news