An improved recent run has led City to the brink of the Uefa Cup quarter-finals after an impressive 2-0 victory over Danish side Aalborg in Thursday's first leg.
They travel to Stamford Bridge to face Chelsea on Sunday, but the Republic of Ireland goalkeeper thinks their fans should not expect City to reach the level Chelsea did swiftly after they were taken over.
"The owners only took over here six months ago," Given said.
"(Roman) 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.
Building"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."
The Eastlands outfit have risen to eighth place in the Premier League but face a tough task against a Chelsea side that is unbeaten since the appointment of interim manager Guus Hiddink.
Given is well aware of how difficult it will be for City to avoid defeat, even though he managed to keep a clean sheet when playing at Stamford Bridge for Newcastle earlier this season.
He added: "They have improved since Guus Hiddink went there.
"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."