They are hotly anticipated to challenge this season under Alan Pardew, who has turned them into a formidable outfit since taking over at the club midway through last season.
"I think Palace will finish in the top half and push for the top six,” he told Sky Sports.
“I don't think they will get there but I think they'll be between seventh and ninth. That's really a good season and fantastic work for Palace."
Palace forward players make them dangerous
And Neville believes it is Palace’s forward players that will see them challenging for a place in Europe this season.
The star man among that bunch is Yannick Bolasie; with the winger having lit up the Premier League last season with his direct running and skill moves a constant threat to opposition defenders.
They also have the likes of Jason Puncheon and Wilfried Zaha enjoying their football at Selhurst Park, with the latter proving the difference in Sunday’s win, and Neville says those unpredictable players makes them dangerous.
"Palace are on track," he added.
"They are a good side, they have established themselves in the Premier League. They are really dangerous going forward, they have so many instinctive and unpredictable players who do things off the cuff.”