The Blues have been the nearly men of the Champions League for the last six years, being knocked out at the semi-final stage on four occasions and, having at last managed to get through to the final in 2008, losing on penalties to Manchester United.
This year looks like being another good one in Europe for Chelsea, who under boss Carlo Ancelotti have won all three of their Group D games without conceding a goal and have the chance to book their spot in the last 16 with a victory over Atletico Madrid at the Vicente Calderon.
Back on the ball: Cole has returned after his lengthy lay-off
Cole sees no reason why they cannot go all the way this time around.
'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 Cole.
'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 was sidelined by injury last season when Chelsea exited the Champions League in heartbreaking fashion against another Spanish side, Barcelona, losing on away goals in the semi-finals after Andres Iniesta netted a stoppage-time equaliser at Stamford Bridge.
Cole said of that defeat: 'That was the most difficult game to watch for me, I was convinced it was going to be our year. It didn't happen and it hurt, like it would have any other Chelsea fan, but we have to put that behind us now. That's been and gone, and now it's a new season and a fresh chance to win it.'
Whereas Chelsea have never won the European Cup, their main rivals for glory in Madrid next May have tasted plenty of success in the competition down the years, with Real Madrid (nine-times winners), AC Milan (seven), Liverpool (five), Barcelona (three) and Manchester United (three) all proving themselves at this level.
Sickener: Iniesta stunned Stamford Bridge in the semi-final last season
Cole believes if the 2005 and 2006 Premier League champions want to be seen in the same light as those giants, they need to conquer the continent.
'I think it's important for the club, we need to win the Champions League,' the England international 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.'
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