The midfielder was confirmed as a West Ham player on Friday, and registered in time to face Manchester United in the FA Cup third round on Saturday afternoon - a prospect he regards as a "dream".
Cole told reporters: "These are the games you want to play - Manchester United in the Cup. We'd settle for 1-0 but it will be a tall order. It is a tough ask and we'll be giving everything.
"I'm buzzing to play and make my debut again. I'm just looking forward to playing."
The former Chelsea and Liverpool midfielder began his professional career at West Ham in 1999 with his first appearance for the club, but Cole has revealed that he turned down Manchester United when he was only 13.
"Sir Alex Ferguson did want to sign me as a young kid, but I had made my decision to come here as all my pals were here and I was very comfortable here as a youngster," Cole, now 31, added.
"They asked me to go the  Cup final with them, but it wouldn't have been right going along and taking in all the razzmatazz of the day.
"It would have been lovely for a young kid, I was only 13 at the time, to go the Cup final with them, but it wouldn't have been right because I knew I was going to sign for West Ham, so we said no because I didn't want to lead anyone on."