The Hammers are heading back into Europe for the first time since 2006.
The Hammers will be tasting European football for the first time since 2006 having qualified for the Europa League via the Fair Play league at the end of last season.
They will enter the competition at the first qualifying, with the draw pairing them against Andorran side FC Lusitans on Monday, who they will take on at the Boleyn ground on July 2.
While the game should be an easy one to win for new boss Slaven Bilic and his side, Sullivan has warned against overconfidence.
“We can't be overconfident,” he told the official website.
“It is very exciting that the club is back in Europe. Unless we do something very wrong, one would anticipate progressing beyond these first two rounds.”
The owner is wise to warn the fans about overconfidence, with the tie against the Andorran side likely to prove tougher than it looks.
The biggest challenge is likely to be fitness, with the Hammers starting the season much earlier than everyone else as a result of their European adventure, with many likely to be praying it doesn’t have a negative effect once the Premier League is in full swing.