FA chairman Greg Clarke says he is disappointed that a suggested review of inclusion and diversity at board level cannot take place.
Clarke has written to FA Council members to say the board met last week and a number of options were discussed with a view to making the board more diverse.
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"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 professional game representatives on the board are Peter McCormick, the chairman of the legal advisory group of the Premier League, English Football League chairman Rick Parry and Rupinder Bains, who jointly represents the Premier League and the EFL.
The 2017 reforms which Clarke says the professional game representatives deemed sufficient have led to BAME representation on the board reaching 10 per cent, 10 per cent representation from the LGBT+ community 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."
Elliott has created a voluntary Equality In Football Leadership code which aims to improve diversity at decision-making levels in the sport.
Three members of the FA board - Bains, Sue Hough and FA chief executive Mark Bullingham, are supporting Elliott with the work.