Hernandez, who netted eight times in 28 Premier League appearances last season, told the club's official website that the East London side should be aiming higher this time round.
"Top six, top four is the aim, as high as we can [finish]," the Mexican international said. "I am dreamer. I am always aiming as high as I can and if we can put West Ham in the Champions League, why not?
"[Manuel Pellegrini] 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 lineup 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."
Hernandez, who has also featured for Manchester United in the English top flight, has scored 45 goals in 131 Premier League career outings.