The 25-year-old midfielder committed his future to the Hammers this week by penning a new three-year deal at Upton Park.
Noble is the Hammers' current longest-serving player and is now targeting a call-up for Roy Hodgson's England team.
"That's my aim, still, I'm still only 25," he said. "There's a lot of late additions to the England squad.
"The form that I've been in lately, I'm still hoping to get into that squad. If I carry on playing the way I am, hopefully it'll happen sooner rather than later."