The Hammers currently sit in third place after a fantastic start to the campaign.
Talk of a top six, and even a top four finish have begun to emerge after West Ham’s remarkable succession of away wins against Arsenal, Liverpool and Manchester City, but Bilic is determined to keep his feet firmly on the ground.
“I don’t play the targets down, seriously. Nobody is saying we are going to finish fourth," said Bilic, in quotes published by the London Evening Standard.
"What does 'targets’ mean? What are 'targets?’ Targets are for a club like Man United, all my targets are about trying to improve us day in, day out. Where is that going to take us? I don’t know.”
Bilic’s men have far surpassed even what the Croatian would have anticipated after a build-up to the season which focused mainly on the club preserving its Premier League status for the move to the Olympic Stadium.
Sights are now undoubtedly set higher than that, and European football is a distinct possibility with the squad West Ham have put together.
They seem to possess the winning formula away from home and if they can ensure form at the Boleyn improves over the coming weeks, they are sure to be at the right end of the table for a while yet.