The east London club finished 13th last term after managing to come 10th in their first campaign back in the English top flight.
But Hammers co-owner Sullivan wants United to set their targets high in the 2014-15 campaign, even if he concedes that a top-six finish is an ambitious goal.
“You can’t just look to stay up,” Sullivan told The Mirror. “It is not acceptable to our supporters to say, ‘We’ve survived. We’ve had a very good campaign.’
“We are not Norwich. We are not Fulham. We are not Reading. We are West Ham United.
“Our supporters are realistic. They know it is a huge and difficult task to break into the top six. But we must be aiming for that, even if we don’t achieve it.”
West Ham kick off the 2014-15 season with a home game against London rivals Tottenham Hotspur.
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