The Hammers are enjoying their best top-flight campaign in recent memory and currently sit just a point off fourth position and a place in the Champions League qualifying round for next season.
This season, which is the club's first under the management of former Croatia boss Slaven Bilic, has seen the Irons do the double over Liverpool and also beat Manchester City, Arsenal, and Tottenham Hotspur on their way to challenging for European qualification.
Much of the club's success has rested on their marquee summer signing Dimitri Payet and being able to keep hold of key players such as Cheikhou Kouyate and Manuel Lanzini, the latter of whom was snapped up on a permanent deal last week after an impressive loan spell.
Noble, whose testimonial at Upton Park was watched by a season-record attendance on Monday afternoon, believes that West Ham's success on and off the pitch this season shows that they can compete at the very highest level.
He told the Mirror: "We are moving to the Olympic Stadium and we have been told the 54,000 capacity will be increased to 60,000. That shows you the way the club’s going.
"And the money in the game now means we are able to keep hold of our best players. We’ve just signed Dimitri Payet for another five years. We’ve signed Manu Lanzini. We have Cheikhou Kouyate on a long contract. The board have done a great job in getting everyone. That shows you the ambition at the club.
"Obviously we’ve had such a great season this year and it ain’t finished yet. We’ve still got a lot of history to write in the next few months."
The Hammers' fine season has left them on the verge of history in their final season at Upton Park with the club chasing a first-ever place in the Champions League.
When the full squad return to the training ground after the international break they will be looking to continue a run of form which has seen them go unbeaten in their last eight matches in all competitions.