The 32-year-old midfielder has just one full season left on his contract after joining the club in a five-year deal from Aston Villa in 2009 and admits he is settled at the Premier League champions.
"I want to finish my career still challenging for trophies and this is the perfect club at which to do that," said Barry.
"I am very settled here but at the same time I have got a lot of respect for the people who have come in.
"They are going to have a good long look at the way they want to go and the players they want to go with so as individuals we need to work hard when we get the chance."
Barry is referring to new chief executive Ferran Soriano and sporting director Txiki Begiristain, who are charged with shaping City's future in the mould of former employers Barcelona.
With senior players such as Barry, Carlos Tevez and Joleon Lescott all out of contract in 2014, there is uncertainty regarding the future of several senior players but Barry insists they are relaxed.
"Obviously they are the sort of conversations the lads have now and again," he added.
"We've got the rest of this season and then one more year and there have been changes upstairs.
"But everyone is pretty relaxed because they will take time to have a look at things, the way they are going to go in the future.
"The players are pretty comfortable with that too but it is important we keep performing on the pitch."
Tevez, who has yet to discuss a new deal, is due at Macclesfield police station this week to answer bail after being arrested on Thursday on suspicion of driving whilst disqualified.
The charge carries a possible six-month jail term if Tevez is found guilty but Barry does not expect his team-mate's attitude to be affected - as shown by his weekend hat-trick against Barnsley.
"It takes a lot to take Carlos' mind off football and get him agitated," said Barry.
"If you had seen him at training this week, it's as though he has got no problems away from the pitch.
"Nothing really fazes him. In general, if a football player has problems off the pitch the best place to be to get rid of them is on it, either in training or in the stadium.
"It can certainly help take your mind off them for 90 minutes anyway."