The Blues have fared admirably in European football's premier club competition over recent years, reaching the semi-finals in four of the past six seasons and finishing as runners-up to Manchester United in 2008.
However, the top prize still eludes them, much to the disappointment of those connected with the Blues.
Continental glory now represents Chelsea's biggest ambition, and they have made a bright start in their 2009/10 endeavours.
A 100 per cent record in their opening three games in Group D bodes well, and they will have the opportunity to book a safe passage into the knockout stages when they face Spanish strugglers Atletico Madrid on Tuesday.
Cole is hoping Carlo Ancelotti's side can take a positive result from their trip to Vicente Calderon, helping them to move one step closer to their ultimate goal.
"Obviously the Premier League is very important, but for this club the Champions League is a massive target for us. We've not won it yet," said the England international winger.
Experience"We've come close over the last five years and we probably should've won it on a few occasions.
"We have the right people in charge, we have the experience now and we have to come to places like this and win, that's the challenge for us."
Cole also believes that Chelsea must break their European duck if they want to be regarded as a global powerhouse - like Manchester United and Real Madrid.
"I think it's important for the club, we need to win the Champions League," he said.
"We've got everything else we need, we've the players, the manager, the set-up, everything is fantastic. For the club it's very important to win the Champions League.
"Chelsea are building a genuine claim to be as big as the Manchester Uniteds, the Real Madrids, the Barcelonas, the Milans(but) you have to win trophies, and you have to win major trophies.
"Obviously the Champions League is going to help show us as a worldwide club that means business."