The board of the EFL, which includes Carlisle United's John Nixon, has rejected a recommendation that some of its directors should be replaced.
A review of the League's governance proposed that three independent directors should be appointed to the board, in place of three of the six existing club representatives.
Current League directors, though, turned down the suggestion and the organisation said clubs backed them in this decision.
In a statement today, the EFL said: "After careful consideration, the board decided not to support any change to the current composition of the board, as it believed this could undermine the objective of strengthening the relationship between the board and member clubs.
"EFL member clubs expressed their support for the board’s position on this matter at the meeting."
The current League board includes three club representatives from the Championship, two from League One and one from League Two - United's co-owner Nixon.
The proposal to replace three of those individuals with independent direcrors was the "majority recommendation" from the governance review prepared by Jonathan Taylor QC.
A minority recommendation from Taylor's group was that none of the six existing club representatives remain on the EFL board.
Taylor and his review team reported to a League governance working group which consisted of the EFL's Debbie Jevans and Simon Bazalgette, independent directors on the EFL Board, and three EFL club divisional representatives: Nick Randall QC (Nottingham Forest), Mark Palios (Tranmere Rovers), and Colin Garlick (Port Vale, League Two).
The EFL said the report, which was presented to clubs ahead of a meeting today, "recommended a number of changes to strengthen the EFL’s governance procedures" and that these were endorsed by the board and supported by clubs in principle.
Clubs were also given a report following a review by Taylor into the EFL's handling of the Bury FC crisis.
Many fans have criticised the League for the way it dealt with the situation as Bury were eventually expelled from the competition last Augst.
In today's statement, though, the EFL said Taylor's report says the club's demise was caused by a lack of funds and that extra action by the League would not have prevented this.
The statement says: "After considering the steps taken by the EFL at each stage, Mr Taylor concludes that the League spent significant time and effort monitoring the situation at Bury FC and applying its regulations to try to force the Club and its owners to meet their commitments.
"He notes that while it can always be argued, with the benefit of hindsight, that more could have been done, any additional action would not have made any difference to the eventual outcome, which was ultimately caused by a lack of owner funding."
The EFL say the two reports will be published on their website "in due course".