The 33-year-old striker fell out of favour under Gunn last season, but with just a year remaining on his contract insists he can ill-afford to spend another campaign on the fringes.
"I'm at an age now where I want to play as much as possible. It's not like I'm 21 and with my whole career ahead of me. I'm in the last year of my contract and the last thing I need is to have a season like I did last year," Cureton told the Eastern Daily Press.
"That would be no good to me. I would love to be playing every week, scoring goals and earning another contract here, but if that's not the case I have to worry about my future.
"I still feel I have a lot of good years in me and I don't want to hinder that by having another season where I don't play and I don't get goals because then if I don't stay at Norwich, after that my options are limited because I've had two seasons that haven't been great.
"I need this year to be a really big year and hopefully that will be for Norwich, but I don't know."