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"We feel that Halifax do not qualify," said conference general manager Dennis Strudwick.
"There will be correspondence to the club hopefully today or tomorrow."
Mr Strudwick said he had heard nothing from the administrators running the club since Friday when efforts to reach agreement with creditors failed.
He said a Halifax club would now have to be reformed from scratch and seek approval from the Football Association and then be allocated a league to play in.
Mike Appleby, league manager for the FA, said there would be a place for a Halifax team but the issue would be at what entry level.
"We will accommodate Halifax. We are not going to let football die in Halifax," he said.
The consortium and the Halifax Town Supporters' Trust have both indicated they were interested in running a club.
"We have had notice of intent but not the detail" said Mr Appleby.
The detail will now have to be worked up speedily but confusion surrounds the consortium's intent as it has been working behind the scenes leaving fans in the dark.
The trust is now split with some wanting to back the consortium - with its financial standing and business expertise - and others want the trust to run a members' club.
Mr Appleby said whichever group came forward to form a team it would have to prove security of lease.
A team playing at the Shay can expect to compete in the fourth tier of non-league football in the Northern Premier League Division One North (Unibond).
If games are not played at the Shay then the fifth tier Northern Counties East Football League is the likely scenario.