The Citizens, who were last crowned league champions in 1968, have struggled throughout much of the last 30 years.
However, after being taken over in 2008, the club have enjoyed a resurgence under big-spending owner Sheikh Mansour.
The Manchester outfit secured their first ever top-four finish in the Premier League last season, and Barry insists that the team are closer than ever.
"If you look at our finishes, we were 5th, then we finished 3rd last season and won the FA Cup," he told the club's official website. "That is great progression and if you keep doing that then a league title is not going to be too far away for us.
"Players always look at the league table. You never get too carried away by it but you are always looking. We have started well and now the top area of the table is where we are going to aim to stay.
"It is always tough to keep winning but that is the mentality the club need now and the players are trying to adapt to it."
Manchester City are currently second in the Premier League table on goal difference.