Arsenal made light work of North London rivals Tottenham Hotspurs over the weekend, beating them 2-0 at their own backyard.
The Gunners look well on course to end their near two-decade Premier League drought this season after dropping points in just three of their 18 games played.
Mikel Arteta's side are however yet to face champions Manchester City this season and those games will truly test their title credentials.
Neville does not feel Arsenal have what it takes to get the better of Pep Guardiola side, whom he has tipped to retain the title, with Manchester United taking runners up honours.
Asked if Arsenal will win the Premier League, Neville said on his Sky Sports podcast: "No. But I said Leicester City wouldn't win the league...
"I don't think they will win the league. Manchester City will win the league, and I think Man Utd will finish second, and I know that will annoy Arsenal fans.
"I'd rather Arsenal win the league than Man City. I think it would be absolutely sensational for the Premier League.
"I think about watching the Premier League, we've seen City sweep up, apart from Liverpool, over the past five years.
"To think Arsenal could come and win it, it adds to our league, it makes our league great. I'd love Man Utd to win it, but I don't think that's going to happen this season."
"The reality of it is, I think at some point Man City will hit a run. Once they do, they've got to play Arsenal twice," Neville said.
"At some point, there will be a very difficult period for Arsenal this season. Is it conceivable that Arsenal are going to continue as they are? I don't think it is.
"Could they draw two and lose one in a three-game period, and if they did that, their lead is gone, and the pack is up with them? That's what I think is going to happen.
"We'll see a traditional Premier League season where a team goes out, the pacemaker, and then they'll get drawn back in a little bit.
"But I still think that this season is going to be far better for Arsenal than I ever imagined it would be."
