Three sitting judges expressed interest in the job before it was given to the outgoing Attorney General Seamus Woulfe.
Opposition parties have questioned whether the process was run correctly and why candidates with judicial experience were not preferred.
Tánaiste Leo Varadkar has said a recruitment process is not something to be debated on the floor of the Dáil:
"It wouldn't be appropriate for 20 people sitting around the cabinet table to be poring over a shortlist of names and discussing the merits and demerits of each candidate, it wouldn't be fair to them," he said. "And it would probably discourage good people from applying. And that's why I'm counselling against having that kind of debate in this chamber, us discussing the merits and demerits of different candidates, even if they're not named".