Barry is out of contract next summer and has revealed that City players are unsure if new chief executive Ferran Soriano and football director Txiki Begiristain will initiate a mass exodus this summer.
He told The Mirror: "Obviously they are the sort of conversations the lads have now and again. We've got the rest of this season and then one more year and there have been changes upstairs.
"Everyone is pretty relaxed because they (Soriano and Begiristain) will take time to have a look at things and the way they are going to go in the future. The players are pretty comfortable with that, too, but it's just important that we keep performing on the pitch. I want to finish my career still challenging for trophies and this is the perfect club at which to do that.
"I'm very settled here but at the same time I've got a lot of respect for the people who have come in. They're 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."