Co-chairman David Gold has no doubt West Ham will be in a position to frighten the Premier League's leading clubs once they are playing at a packed out Olympic Stadium.
The Irons on Friday launched a new commemorative strip ahead of their final season at the Boleyn Ground before switching to Stratford.
With a capacity of some 54,000 from 2016-17, the Irons will see their match-day revenue dramatically increase, therefore putting the east London club among the top flight's leading earners.
Gold believes that once ticket sales begin to have an impact on the field West Ham can become a force to be reckoned with.
"We are hoping West Ham will be in a position very soon to worry the top five and have them saying: 'Who are these upstarts? Who do they think they are?'" he said. "As far as challenging these great clubs, it is very, very hard. Southampton challenged last season, and there is absolutely no reason why West Ham can't emulate them.
"There is a big difference between realism and hope. Realistically, in the next five years we would expect to be knocking on the door of Europe, whether that is by finishing seventh or eighth or by winning the FA Cup."