The former England international is eager to point out that he is not accusing those at the Etihad Stadium of buying success.
Considerable investment has been made by a club backed by billionaire owner Sheikh Mansour, but a number of domestic rivals have also spent big in recent transfer windows.
City have been able to stay ahead of the pack, claiming back-to-back titles and closing in on a clean sweep of English honours in 2018-19, with Pep Guardiola looking to establish an era of dominance.
Barnes fears they will be successful unless measures are taken to curb the power of those with the deepest pockets.
He told the Irish Independent: “I am a firm advocate of a salary cap as that will instantly begin to level the playing field.
“When I suggest this, people always say it can't work and clubs would find a way of getting around it, but it has been effective in other sports around the world and I don't see any reason why football cannot follow suit.
“What a salary cap would do is encourage clubs to invest in young players and change this culture of signing five players every summer for millions upon millions and if those signings don't work, rip it up and start again in the next transfer window.
“This is not a criticism of Manchester City and the position they are in now because clearly they are a fantastic team led by a great manager and even though they have more money than anyone else, they have still had to be wise in the way they have spent it.
“It is too simplistic to say City have bought the Premier League title or that they have bought the treble if that is what they do this weekend.
“A lot of teams have spent big money in the last few years and not managed to achieve the success of City, so you have to congratulate them on what they have done.
“However, the potential is there for City to dominate English football for years to come unless something is done to change the structure of the game and control the way clubs manage their finances. I think a salary cap would do that.”
The Football League abolished wage cap rules back in 1961 and have not reintroduced them since, despite Financial Fair Play regulations being put in place to prevent clubs from spending beyond their means.