The Gunners, who finished runners-up to Leicester City last term, have not made the type of signings that fans craved at the end of the 2015-16 season, with midfielder Granit Xhaka - signed for £34 million - their only established incoming so far.
Arsenal boss Arsene Wenger has so far failed in his efforts to recruit a top-drawer striker despite bids for Jamie Vardy and Alexandre Lacazette this summer, meaning much-maligned Olivier Giroud is almost certain to start the new campaign as their first-choice hitman.
Arsenal manager Arsene Wenger
Liverpool, on the other hand, have been more active than their North London counterparts, with manager Jurgen Klopp splashing some £60 million on six signings so far - including Sadio Mane and Georginio Wijnaldum.
It might well be the toughest Premier League season to date after managers Antonio Conte and Pep Guardiola joined Chelsea and Manchester City, while Jose Mourinho returned to English football to replace Louis van Gaal at Manchester United.
Nevertheless, Neville believes Klopp will mark his first full season as Liverpool boss with a top-four finish, while predicting Arsenal will finish behind Mourinho's United in the title race.
"I will say Manchester United for the title with Arsenal in second, Manchester City in third and Liverpool fourth," he told Sky Sports.
"But if anybody is reading this and thinks I know what I'm talking about, then I need to make it clear that I really don't have a clue!"