The former Newcastle and Liverpool frontman is out for an indefinite period of time because of a heel injury, with the Hammers keen on not rushing their £15million summer signing back into action.
Carroll's primary focus is to repay the faith that the London club have shown in him when he does return up front and hopes that will be enough to earn international recognition.
England qualified for Brazil 2014 earlier this week by beating Poland to finish top of Group H.
"The lads did a great job and it's brilliant that England will be in Brazil," he said in the Daily Mail. "It also gives me something to aim at and, once I get back playing, I might have a chance of breaking back into the squad.
"The first objective, of course, is to get back playing well for West Ham. I want to do that because they've been so supportive but if England follows, that would be good, too."