City visit Stamford Bridge tomorrow on the back of an improved recent run, culminating in a stylish win over Aalborg on Thursday that has taken them to the brink of a place in the Uefa Cup quarter-finals.
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After 33 years without a trophy, the prospect of silverware is a pretty appealing one to the City faithful who are starting to see the vast fortune of their Abu Dhabi-based owners pay dividends.
A visit to west London is bound to bring reminders that Roman Abramovich had only been in control for two years before he was able to celebrate the first of his two Premier League titles.
Yet Given feels the 'battle of the billionaires' is slightly uneven at present – and that it may be a little while before City are operating on a level playing field.
"The owners only took over here six months ago," observed the Republic of Ireland star.
"Abramovich has been there for a number of years. They were an established team even when he took over and he has added a lot of quality.
"You do need the big backers behind you, which thankfully we have got. But we have not really flexed our muscle just yet.
"We are still in the early stages of building and it might take a little bit of time. But there is no reason why we cannot look up to them and try to get there."
Although City have not won a Premier League away game since August, they do not have to look that far back for a decent result on their travels, having grabbed a point at Liverpool less than a month ago.
In addition Given was part of the Newcastle side that secured goalless draws at Stamford Bridge and, prior to that, Old Trafford earlier this season, which proves nothing is impossible, even if Chelsea are a rejuvenated force under new manager Guus Hiddink.
"They have improved since Guus Hiddink went there," said Given.
"They already had some good players there and Hiddink is a fantastic coach. He has given them more belief and that will ensure it is a tough game for us."