West Ham United take on Bournemouth and Newcastle United in their next two fixtures.
The Hammers’ co-chairman has set the team a modest target of picking up two points from their next two matches, which are both away from home.
West Ham first take on Bournemouth tomorrow, before they face Newcastle United on Saturday.
And Sullivan said: "Any away points are good so two would be an achievement but I don’t see any reason why we couldn’t get four from those two games.
"If we’re going to keep looking up the table that’s what we must aim for. These are very exciting times."
West Ham go into the matches unbeaten in their last eight contests across all competitions.
The Hammers have been in excellent form, and have proven very difficult to beat all season.
With many of their key players now returning from injury, Bilic’s side are only set to get stronger - and they are already in a commanding position in the Premier League table.
West Ham occupy sixth spot in England’s top flight and they are competing for a place in Europe.
Bournemouth and Newcastle, meanwhile, are both battling against the drop, and are in 16th and 18th place, respectively.