The Blues midfielder admits Europe's premier competition has become the club's Holy Grail after more near misses than he cares to remember.
Cole said: "It's so important for Chelsea as a football club to win the Champions League.
"If we are building ourselves up as a club as big as United, Madrid, Barcelona or Milan, then we have to win major trophies.
"Everything else is already in place - the players, the manager, the whole set-up is fantastic. But the Champions League will help us as a worldwide club, to show that we're here to do the business.
"The Premier League will always be very important to Chelsea, but the Champions League has now become a massive target for us all.
"We have come very close in the last five years and maybe we should have won it on a couple of occasions."