Institute's decision not to apply for a Uefa licence means there may be no seventh-placed team in the Irish Premiership's Europa League play-offs.
Eighth-placed Stute trail Glentoran by two points ahead of their head-to-head match at the Oval on Saturday.
If the north west club overtake the Glens then neither side would contest the end-of-season European play-offs.
The IFA also say they are assisting Irish Cup finalists Ballinamallard's request for an extraordinary licence.
"The licensing process for this cycle has still not concluded as we continue to work with Ballinamallard United FC to submit its 'extraordinary' UEFA Licence application (for non-top flight clubs) to the UEFA Licensing Administration in the days ahead," said Allen McKinstry, chair of the IFA licensing committee.
"Whilst the Ballinamallard United FC players will look to create history in the Irish Cup Final, the Ferney Park administrators could also create their own little bit of history if they become the first club to secure a licensing hat-trick with Championship, Promotion and UEFA licences all in one season. The committee wishes the club well in that process."
Newly-crowned champions Linfield, who will contest the 2019/18 Champions League qualifiers, are among eight Irish league sides that have been granted Uefa club licences.
Ballymena United, Cliftonville, Coleraine, Crusaders, Dungannon Swifts, Glenavon and Glentoran have also met the standards to compete in European competitions next season but Warrenpoint Town's application was refused.
Institute, who have again applied to play their Premiership matches at the Brandywell Stadium next season, passed up the opportunity to request a Uefa licence, which has created the possibility of three, four or five clubs taking part in the Europa League play-offs.
If Crusaders win the Irish Cup to secure a Europa League spot and Glentoran finish seventh in the league position then four teams would compete in the play-offs - Glenavon, Cliftonville, Coleraine and Glentoran.
If Crusaders win the Irish Cup and Institute finish in seventh place then only three teams - Glenavon, Cliftonville and Coleraine - would compete in the play-offs with the highest ranked club receiving a bye into the final.
A historic Irish Cup final win for Ballinamallard would see Crusaders enter the play-off draw, which could also feature Glentoran if they secure seventh place.