Bilic signed a three-year deal at West Ham when he took over in the summer, and his bright start at Upton Park has already led to calls for his contract to be extended.
However, Sullivan has urged caution, and he says that Bilic is unlikely to be offered new terms for at least another 12 months.
"Judge every manager over three years but I think we have got a very good one," Sullivan said to the Daily Mail.
"He played for the club, knows what the supporters want, knows that the FA Cup is important to us. He tries to play good football.
'Yes, it's possible that we could review his contract and do something in the summer. But it's more likely that we would do it next January. You do get one-season wonders, after all."
Bilic already has more support than his predecessor, Sam Allardyce, ever did at Upton Park due to his impressive start.
The Hammers have played flowing football throughout the season, with creative players such as Dimitri Payet and Manuel Lanzini both able to thrive.
Bilic has led the Hammers to wins over the likes of Arsenal, Manchester City and Liverpool already.
West Ham are currently in sixth place in the Premier League table, with suggestions that they could claim a European spot becoming louder.