The Hammers are currently seventh in the standings after taking 10 points from their opening seven matches of the campaign.
Despite there being over 30 games of the campaign left to play, Sullivan is confident that they can remain around the European places.
"I've said right at the start we can finish sixth and I think it's possible," he told the club's official website. "We could be on 18 points now. It's not a dream - we just needed a bit of luck in three games where we didn't get what we deserved. I don't think we've had a single game this season where we got more than we deserved out of a game.
"I also realise things can go wrong but I think there are grounds for optimism. It's not rhetoric based on nothing, it's based on what we've achieved so far and the fixtures we've got coming up. If we play them like cup finals and play the West Ham way and score some goals, we could be in the top six."
West Ham return to Premier League action on Saturday when they travel to struggling Burnley.