Mr John White, acting general secretary of the ASTI, is now widely expected to replace Mr Charlie Lennon as general secretary.
This follows a meeting of its executive which decided to use an interview process to fill the role.
In a significant move, the weekend meeting decided overwhelmingly against choosing Mr Lennon's successor by means of a national ballot of its members.
Although Mr White enjoys strong support among the grassroots membership, such a ballot could have given way to an election campaign in the bitterly divided union.
However, following Saturday's meeting, a nine-member team will now select and interview candidates for the job and will then submit its decision to the teaching union's central executive for ratification.
The interview board will be made up of members of the ASTI's executive and its four officers.
Sources at the union were last night unclear as to when the selection process might begin, although some suggested the new general secretary could be in place by October next.
All five executive members on the interview board are from outside the Dublin region, and many are thought to be supporters of Mr White. They will be joined by its four officers.
However, although the race to succeed Mr Lennon is certain to include at least one of these officers, in the form of Mr White, the procedure to deal with this scenario has yet to be decided.
Previously, the ASTI had said it would consider the possibility of a national ballot, similar to the approach taken by the INTO.
However, a report presented to the executive was overwhelmingly rejected in favour of the interview panel approach.