David Moyes' in-form side are currently third in the Premier League, ahead of Liverpool thanks to their 3-2 win over the Reds, and level on points with Manchester City after 11 games.
This is no purple patch, though, since West Ham finished sixth last term and currently stand unbeaten in their Europa League group.
The Hammers' dramatic upturn in fortune, from relegation battlers to genuine European contenders, has seen the rise of a new slogan - 'we are massive' - perhaps in jest more than anything else.
But with their stadium soon to become the third largest in the top-flight and results to match the very best in the land, many would struggle to argue right now.
Even Gabby Agbonlahor, the Aston Villa legend, recently called them the second-biggest club in London, above Arsenal and Tottenham but behind Chelsea.
However, former Crystal Palace owner Jordan insists their current achievements aren't enough to put them alongside the giants of English football.
In fact, he suggests Hammers supporters might be better considering themselves a smaller club overachieving, rather than setting up to fail.
"You open yourself up to ridicule by putting these sort of statements out," Jordan told talkSPORT.
"It's a mission statement as well as a glowing endorsement of what they're currently achieving.
"It's like money talks and wealth whispers, isn't it? You're being judged by overachieving, rather than setting yourself a standard and then underachieving against it.
"West Ham have a massive fanbase. They have a massive stadium. They're increasing the size of their stadium. Their achievements are massive at this moment in time, in comparison with West Ham's achievements of recent times.
"But that doesn't make them massive, by comparison to clubs who are really, genuinely, bonafide massive. That's Man City and their achievements. Liverpool and their achievements and history. Chelsea in their recent history.
"What we're saying, really, by looking at this, is are you getting a bit ahead of yourselves?"