Under-19 manager Dave Connell was previously overlooked for the senior role in 2019 when Vera Pauw replaced Colin Bell.
He has been in charge of the underage side since 2011 and has twice reached the U19 Euros.
In 2014, with a talented squad that included the likes of current senior captain Katie McCabe as well as Courtney Brosnan and Megan Connolly, they reached the semi-finals.
The current crop of U19s bowed out at the group stage this summer, but did claim a famous draw against eventual winners Spain.
With 13 years of experience with the U19s, Connell has already coached the majority of the players who have progressed into the senior squad and could help bring through the next generation.
The former right-back was player manager at Limerick between 1997-1999 and also had a four-month spell as Galway boss in 2001.
His lack of senior managerial experience may be a concern, but if the FAI want an in-house appointment for continuity purposes he will be in with a chance, especially given the financial difficulties at the association which may impact their shortlist.
Connell is expected to step up and take interim charge of the senior squad for their opening Nations League games against Turkey and Slovenia in February if the FAI have not appointed a permanent successor to Gleeson before then.
Those games may act as Connell’s audition to landing the job permanently, as the previous round of Nations League games did for Gleeson last year.