The clubs do not want to do anything which would compromise their places in the English pyramid and have sent a letter to the FA seeking assurances over their participation in the English system.
The matter is also set to be discussed at the next meeting of the Professional Game Board (PGB), a committee of the FA board that handles subjects related to the Premier League and Football League (EFL), who have representatives on the PGB.
Prosiect Cymru has been presented as a path to a “transformational change” in Welsh football.
The idea emerged from a report by Deloitte, commissioned by Swansea City. Wrexham are also in favour, while Cardiff City are supportive of the dialogue.
But the issue is considered to be most sensitive for League Two club Newport County.