Sullivan and his fellow board members announced last week that they would be keeping Sam Allardyce on as manager next season.
While the Hammers endured a disappointing 2013-14 campaign, Sullivan hopes that some fresh faces at Upton Park will help the team to improve when they return to action in August.
"We want results, goals and entertainment and if we just get a couple of the players we hope and think we will get, these are players who the supporters will find exciting," he told the club's official website.
"They will love to see them, players who like to go past their defender, go into the box and slot it into the bottom corner or whack it in from the edge of the box.
"We hope to sign a striker next week and he is a fantastic player. He takes people on and he can be a special player, then we have got other players as well."
West Ham finished last season in 13th place in the Premier League table.