Cole was set to join Stoke, but despite the clubs agreeing a £6million fee, the player decided to stay put with promotion hopefuls West Ham.
Cole, who has hit 14 goals this term, said: "It would mean the world to me to take West Ham back to the Premier League.
"That is the task I had at the start of the season, I could have left but there was no point because I'm so happy. I wanted to make an impact and help the team get to where we belong.
"It would mean a lot to reach Wembley. They say that the best way to go up is to win the play-off final. Hopefully we'll do that."