Cole is now in his second season back at the Boleyn Ground.
"There will always be the street footballer inside of me," he told the Daily Express. "But you want to do something more than that in the game. You want substance and impact. I got that at Chelsea. That is why it would be so special to win some silverware with West Ham.
"I'm lucky enough to know what it feels like. And I saw the fans at the 2006 FA Cup final, when they came so close.
"To win something with a group of supporters who keep the faith like that even though they have been starved of success would be so amazing.
"I hope I can give the fans some big moments here yet."
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