The Show Racism the Red Card organisation has issued a call for a meeting following the boycott of the Kick It Out T-shirt campaign by a number of players at the weekend.
Anton and Rio Ferdinand and Jason Roberts were among those who refused to wear the T-shirts before Premier League games.
The players are apparently unhappy with Kick It Out's response following the recent high-profile racial abuse cases.
Show Racism the Red Card's statement read: "We fully understand the anger of the Ferdinand family and Jason Roberts in relation to the FA handling of the John Terry case. Both Rio and Jason are long-standing patrons of our campaign and are recognised in our Hall of Fame for their work.
"The issue of not wearing the Kick It Out shirts at the weekend highlights the displeasure of certain players in relation to the footballing authorities' handling of the incidents of racism in the game.
"We call on the players involved to now sit down with us, KIO and the PFA to draw up a plan of action to present to the footballing authorities and government."