The Gunners have yet to get their hands on the most illustrious piece of silverware in European football's trophy cabinet, with a final defeat to Barcelona in 2006 as close as they have come.
Arsene Wenger's side are, however, on the march in 2012/13, with a 2-0 victory over Montpellier on Wednesday seeing them safely through to the last 16 with a game to spare.
Szczesny is now setting his sights on going all the way, with it his opinion that Arsenal can emulate Chelsea's achievements from last season and conquer the continent.
He said in the Evening Standard: "Of course we have (taken inspiration from Chelsea). They weren't fantastic in the Premier League last season had a fantastic run.
"I hope we can do what they did last season but do a little better in the Premier League as well.
"You only take part in competitions to win them. There are fantastic teams in Europe and ones probably more likely to win it than us. But I'm in this competition to win it, so that's my ambition."
Arsenal still have one more group stage fixture to take in this season, but Szczesny refuses to buy into the belief that victory over Olympiakos and top spot is a necessity.
He added: "Arsenal have qualified for the last 16 every year for the last few years and I don't think us qualifying is a surprise. Chelsea and Man City not doing well is a massive surprise. At the moment, we are just enjoying that we got through and that is what we're going to focus on.
"Of course, we hope to get a good result but it's not in our hands, we have to rely on someone else to get results as well.
"I'm not sure it's the most important thing to finish top. In the last 16, whether you finish first or second, you come up against the best teams in Europe. We finished top last season and played AC Milan away and lost 4-0."