Portadown's appeal against an Irish FA decision to reject their application for a place in the new Premier League is being heard on Monday evening.
The IFA ruled the application could not be considered as it had been received 14 minutes after the deadline.
Limavady United's appeal against the decision not to grant them a domestic licence has been rejected.
Other clubs believed to be in danger of not making the new league are Donegal Celtic, Institute and Bangor.
If Portadown lose their appeal, that would still leave one of Donegal Celtic, Institute or Bangor missing out.
BBC Sport understands that the composition of the new league is likely to be announced on Tuesday evening.
On Monday, the IFA announced that an appeal by Limavady United against the decision not to grant the club a domestic licence had been dismissed.
Limavady's application was submitted several weeks late.
Portadown claimed their documents were 14 minutes late because of a traffic accident.
606: DEBATE
Club vice-chairman Bobby Jameson said the club's accountants had been aware of the deadline which was 1600 on 30 March and that they had proof they had been held up by the road accident.
If Portadown are excluded, the new league, supposed to be more attractive and professionally-run, will kick-off without one of Northern Ireland's leading clubs.
Since 1990, the Ports have won the league championship four times, the last being in 2002.
They are currently building a new stand, part of a £1.75m upgrade at Shamrock Park.
It is believed that, if Portadown are not in the top flight, they will lose some of their best players.
And the Premier League's longest-serving manager Ronnie McFall would also face the prospect of preparing his side for intermediate football next term.
Limavady's appeal was heard by the Licensing Appeals Body chaired by barrister Finbar Lavery.
The Roesiders argued that they should be allowed an additional discretionary period to enable them to finalise their submission for a licence due to the exceptional circumstances they found themselves in following the resignation of their club secretary.
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