The 35-year-old thinks an injury-free season could see them finish in the top six, while suggesting the win over Manchester United gave them confidence for the Aston Villa game
David Moyes' men have shaken off their tag of slow starters this campaign by recording a maximum six points from their first two games, including a win against Manchester United in their opening fixture.
Their start has left many suggesting they can secure a place in the Europa League this term, with the 35-year-old agreeing it is a possibility as long as the squad stay healthy.
"If we can keep everyone fit, we can be challenging for European football," Neville told the Daily Star.
A first win at Villa Park in seven years maintained the Toffees' impeccable start, with Marouane Fellaini and Steven Pienaar in particular impressing. The latter opened the scoring just three minutes in with the Belgian adding a second after half an hour.
Nikica Jelavic made it three just before half-time, and although the Merseyside outfit had to fight-off a potential late come-back when Karim El Ahmadi made it 3-1 with 15 minutes to go, they held on for their second win of the season.
The Everton captain admitted that things became tense when the Villans pulled one back, however he indicated their own display over the Red Devils the week before gave them confidence to see out the game.
"The early goal really knocked Villa," he added. "They wanted to impress under the new manager at home and we knew that.
"You could sense the nervousness crept in and we knew from last year that we could control the game.
"Last year here you could sense the anxiety. We knew they were going to give it a go but after our result over Manchester United, we knew it was all about us."