The Canaries dropped into the Championship last season, along with Cardiff City and Fulham, but have scooped 13 points out of a possible 18 as they aim to bounce back.
Jerome moved to Carrow Road in the summer after falling out of favour at Stoke City, where he spent three years of his career.
"The door was closed on me at Stoke, but here I'm getting fitter by the day," The Express quotes Jerome as saying.
"I haven't set myself individual targets. The only target I have is for the club to be promoted. That's all that matters."
Jerome contributed with a goal in Norwich's 4-2 victory over former club Cardiff on Saturday.