The Hammers are set to modify the stadium to a 54,000 capacity all-seated arena, meaning only the Emirates and Old Trafford could better the possible attendance rates in the Premier League.
Cole believes that the extra revenue, and the classification of the new stadium as a Uefa 'category four' venue, could help the club compete with Arsenal and other top sides.
The 31-year-old told reporters: “To be still here in 2016, and have my family come and watch me in a sold-out stadium, that would be a very proud moment for me.
“I’ll be 34 then. I keep myself fit and want to play as long as I can because I love playing and I’d like to be playing here.”
Cole added: “I think this is a momentous day for the club - one of the biggest in the club’s history.
"It gives the club the opportunity to compete at the top level, with the likes of your Arsenals - clubs that have got stadiums of this size.
“The dream is to one day win the title at a club like this. I have played abroad and people love living in London and a London club with this type of stadium will be able to attract players.”
Despite the move provoking critcism from some West Ham fans, Cole has defended the decision.
“It will always be West Ham,” he said. “Loads of teams have changed stadiums over the years and it is not about where you are but what is in your heart.
“West Ham have a rich history and that isn’t going anywhere because we are moving a few miles up the road.
"It is going to be great - the fans will love the stadium, I am sure.”