"It could be a good year if it ends up with Palace in the Premier League and the fans happy," Hodgson told BBC Sport on Friday.
"I believe the team will stay up. Absolutely. I wouldn't have taken the job if I didn't believe that, or that me and my coaching staff would be the people to do that.
"It's a chapter in the book of life opening for me, and one I'm looking forward to. One I'm hoping brings joy to the fans of Crystal Palace. That would be special because I am a Croydon boy and didn't leave here until I was 24 years of age."
Palace face Southampton at Selhurst Park on Saturday before taking on Manchester United, Manchester City and Chelsea in the league in quick succession.