FA chairman Greg Clarke claims Premier League and EFL chiefs have blocked attempts to review the diversity of the FA board.
Clarke has written to FA Council members to say the board met last week to discuss options to make it more diverse.
"We discussed a number of options including: making the chair of the inclusion advisory board (Paul Elliott) a director and giving the professional and national games an extra board seat each that could provide the flexibility to allow appointment of diverse candidates should they be the best qualified person for the role," Clarke wrote.
"Both our independent directors offered to stand down to create opportunities for a more diverse board but the board was united in declining their offer.
"The professional game were against such a review, believing the changes introduced in 2017 were sufficient. The national game were sympathetic to a review and consultation with Council but did not want to oppose the professional game.
"However, without the support of the professional game and national game, who have a majority of directors, a review of the FA board composition is not possible."
The board's professional game representatives are Peter McCormick, chairman of the legal advisory group of the Premier League, English Football League chairman Rick Parry and Rupinder Bains, who represents the Premier League and EFL.
The changes from 2017 which Clarke says Premier League and EFL chiefs deemed sufficient have led to BAME representation on the board reaching 10 per cent, representation from the LGBT+ community reaching 10 per cent and 40 per cent representation by women.
Clarke added: "I had hoped that the FA, as the game's governing body, would have been able to examine whether its own board was appropriately constituted to represent a diverse game and share its thinking with Council.
"This process is happening across football but will not now happen with respect to the FA board.
"As FA chairman this disappoints me, as leader of Council I felt honour bound to inform you of the situation. It seems to me better to be open on the issue now rather than surprise Council when Paul Elliott publishes the recommendations of his working group in October."
Piara Powar, the executive director of the anti-discrimination Fare network, criticised the Premier League following Clarke's claims. He wrote: "Hey @premierleague you used your veto to block a qualified black person joining the FA board.
"We know you support #BlackLivesMatter it appeared on the backs of players shirts. Show that wasn't an empty gesture, let qualified people sit around the top table. Share power."
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