But the idea has received at best a luke warm reception.
Professional Footballers' Association chairman Clarke Carlisle warned a new group could have a divisive effect. He said unity not separatism was needed.
"[A new body] has the potential to be divisive because when you establish a black players' union it would instantly define 'us and them' and that's something we really need to work against," the York City defender said.
Carlisle also said he had spoken to Reading striker Jason Roberts about the issue after more than 30 players refused to wear T-shirts supporting the Kick It Out anti-racism campaign at the weekend following Roberts's remarks that some black players were unhappy with the organisation's progress.
Football Association chairman David Bernstein urged caution and said a breakaway organisation would not be the best way to deal with racism in the game.
"Fragmentation isn't in anyone's interest. Great passions are involved here. I hope sense prevails and people can work together," said Bernstein.
He also confirmed sanctions for players found guilty of racist abuse would be re-examined in light of the Terry case.
"It's on the agenda to look at it again. The FA received a certain, probably limited degree of criticism for its processes in the Terry thing. We will look at that.
"I think the tariffs will need looking at but, given the existing scenarios and given other punishments elsewhere, actually the commission got it pretty much right."
Gordon Taylor, head of the Professional Footballers Association, which represents all players, told The Daily Telegraph he was dismayed by reports of a possible breakaway.
"I feel we are imploding," he said. "The longer it goes on, the more divisive it is becoming... If they want their own particular select group who they feel they can influence everybody more than the whole PFA as a union together, I would say they are seriously mistaken."
FTD's John Booth commented:
'We are heavily involved with a couple of league clubs as consultants at the moment and the idea that you would 'split' a dressing room with seperate player associations is divisive. Most clubs have a nominated PFA rep who is a link between the players and the club. I find it hard to see how this would work if you had separate representatives trying to do the same job for different sections of a squad especially if they had opposing views on an issue'