It means that the extra eight clubs needed to make up a fifth tier of 20 teams – with the working title of League Three – are likely to come from the National League, formerly known as the Conference.
The 72 clubs below the Premier League which make up the EFL made their stance clear to chief executive Shaun Harvey in talks on Thursday. A final vote on changes to the league structure is set for June.
Harvey said: “The logical place for many was to source the additional teams for League Three from the National League but we felt it important that the debate was introduced at an early stage and an opportunity was provided for all club owners and executives to voice any opinions and, where applicable, table concerns.
“In addition, our dialogue will continue with the Premier League as we focus on ensuring we achieve our specific and primary objective of improving distributable revenue to our clubs and reaching a format that benefits the EFL, its competitions and the wider professional game.”
The idea of including Premier League B teams was suggested by former Football Association chairman Greg Dyke’s commission in 2014.
Old Firm pair Celtic and Rangers have repeatedly been linked with joining English competition.
EFL chiefs announced plans for a shake-up in May as they seek to balance demands to relieve fixture congestion while safeguarding the financial position of their clubs.
A winter break of the type commonly used in other European leagues has also been mooted, although EFL clubs have indicated they would not want the move to be implemented in their four divisions.
Any proposed changes require the backing of 90 per cent of current EFL members, which equates to 65 clubs.