The 27-year-old made 20 appearances for the Three Lions at Under-21 level, but he has never received a call-up to the full side.
However, having impressed during Saturday's 2-1 win over champions Manchester City in a match that was watched by England manager Roy Hodgson, Noble is hopeful that he may be included in the selection for next month's international matches.
"Fingers crossed. Obviously it helps when the team is playing well and sitting in third or fourth place in the league," the Newham Recorder has quoted Noble as saying. "I am pretty sure he was watching Stewart Downing as well as he has been in great form, but hopefully it happens this time."
Noble has scored one goal during his eight appearances in all competitions for West Ham this season.