If adopted, it would mean the Football League becoming a four-division competition below the Premier League, including a new League Three, with 100 clubs in the professional game.
After a meeting of the 72 clubs on Thursday, the EFL rejected the idea of including Premier League B teams in the proposed restructuring, called 'Whole Game Solution', along with clubs from non-English leagues and those from outside the English football pyramid.
"At the very outset of this process it was made clear that any decisions in respect of the future direction of the Whole Game Solution would be taken by clubs themselves," EFL Chief Executive Shaun Harvey said in a statement.
"I am extremely grateful for their candour and support during the first part of this consultation that will ultimately help shape a final proposal for voting on in June next year."
The EFL will now continue talks with the National League, which is the only option left to it for sourcing additional teams for the proposed League Three.
The potential introduction of a winter break also came up for discussion at the meeting with clubs in the third and fourth tier saying they are keen on playing through any proposed winter break.
(Reporting by Nivedita Shankar in Bengaluru; editing by Sudipto Ganguly)
