Hodgson has been out of work since stepping down as England manager after a disappointing Euro 2016 where the Three Lions were knocked out by Iceland in the last 16.
However, Puncheon believes that the former Liverpool, Inter Milan, Fulham and West Bromwich Albion boss has the quality and managerial experience to improve the Eagles.
"He comes with a wealth of experience," Puncheon told Sky Sports News.
"He's managed some big, big players and he's managed in a wide range of leagues. He was the national manager for our country and that speaks volumes for itself.
"Structure is [going to be] important to help us push forward. We've got good players and we've got a good structure that has helped players grow and improve in the past."
Palace are yet to score in the league this season and have conceded seven goals in their opening four games this term.