The former Manchester United star, who played 242 games for Everton during eight years at Goodison Park under David Moyes, is warning rival clubs not to underestimate the Blues.
Another former Everton player, Peter Reid, said on BreatheSport.com that Martinez's side are not getting the credit they deserve and look set to upset the more established sides.
'Great chance for Toffees'
And Neville agreed responding to Reid's comments with confidence on the social networking site.
He said: "Great chance for the toffees this season - I look at the squad and think top four is a possibility!"
Great chance for the toffees this season - I look at the squad and think TOP 4 is a possibility!! https://t.co/eP1Q4hFlX4— Philip Neville (@fizzer18) December 8, 2015
With the likes of Romelu Lukaku, Ross Barkley and John Stones in fine form the Goodison Park out fit look as good a bet as any of the top 10 to make a genuine challenge for the Champions League spots.
Sitting in ninth on 22 points it is probably a step to far to argue the Toffees could mount a title challenge.
But they slowly seem to be finding their feet this season and play some of the best football in the league on their day.
Two points per game average needed
Recent draws against Bournemouth - where they twice threw away the lead to draw 3-3 - and against Crystal Palace on Monday could prove costly at the end of the season, though.
To finish in the Champions League spots Everton will need to maintain a near two points per game average from here on in.
Reid and Neville believe they can do it, now it is up to Martinez and his players to prove it, starting away at Norwich City on Saturday lunchtime.