The 'Hammers' have enjoyed an eye-catching transfer window this summer, bringing in the likes of Jack Wilshere and Felipe Anderson.
Despite battling against relegation for most of last season before finishing 13th, Hernandez says he is aiming high this season.
"Top six, top four is the aim, as high as we can," he told the club's official website.
"I'm a dreamer. I am always aiming as high as I can and if we can put West Ham in the Champions League, why not?"
Hernandez suffered a frustrating first season at the London Stadium after joining from Bayer Leverkusen last summer, but he says he is confident things will be better this time around.
"The manager called me before the World Cup because he knew my situation was difficult at the end of last season, and he made me feel very good," 'Chicharito' explained.
"He told me I was going to be an important player and would play an important role in this team, so he gave me a lot of confidence.
"I'm very motivated and I know I need to work hard to win a place in the starting line-up and then perform as well as I can to help the team with goals, assists and good performances to get the points to move up the table."