Twice champions Sydney have played in sky blue, the state colour of New South Wales, for 10 years, while Heart have played in red and white stripes since they entered the league in 2010.
Manchester City led the consortium which bought Heart in January and are expected to change the club's name after registering the business name Melbourne City FC with the local authorities and buying the domain name MelbourneCityFC.com.au.
The English Premier League club last year established New York City Football Club, who will play in sky blue when they enter the Major League Soccer competition next year, and Melbourne are expected to follow suit.
"In a competition with only 10 teams, the idea of two teams wearing sky blue is nonsensical especially when sky blue is so closely associated with NSW," Sydney FC Chairman Scott Barlow told Tuesday's Sydney Morning Herald.
"I believe it's critical to the integrity of the A-League that clubs have identities that are also in representation of where they come from.
"We're extremely concerned about the proposed use of sky blue by Melbourne Heart, and we've made our concerns very clear to the FFA."
Football Federation Australia (FFA) would have to approve the rebranding of Melbourne Heart, and Sydney FC are not the only interested party opposed to the colour change.
Banners at recent Heart matches and a social media campaign run by fans have urged the new owners of the four-year-old club to "Keep Melbourne Red and White".
Heart finished bottom of the A-League after a 3-2 home defeat to Western Sydney Wanderers in their final game of the regular season last weekend, which attracted 10,000 fans for Harry Kewell's last match.
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