Ms Fitzgerald has received a report from senior counsel Dominic McGinn, who was appointed almost a year ago to carry out an independent examination of facts in the case.
In 2010 the Garda serious crime unit re-opened the historic case but the two-and-a-half-year probe that followed failed to result in any new charges or prosecutions being brought.
Mr McGinn was appointed in December last year to examine the findings of the Garda cold case review.
Now Ms Fitzgerald has confirmed to the Dáil that the review is now completed and is being considered by her department and the attorney general.
“My department has recently received a report from Mr McGinn and is considering it in consultation with the office of the attorney general,” she told the Dáil last Thursday.
While welcoming the completion of the review, the family of Fr Molloy has expressed their disgust at the minister and her department’s failure to notify them of the completed report.
The Molloy family only learned of the completed report by chance when a family member stumbled on an online story about the review yesterday afternoon.
Henry McCourt, a nephew of Fr Molloy’s, said the family was appalled by the lack of communication.
The death of Fr Molloy at the home of his friends, Richard and Therese Flynn, in Clara, Co Offaly on July 8th 1985 has raised more questions than answers for almost three decades.
The historic case has led to questions about the initial Garda investigation, the criminal trial that followed in 1986, and subsequent allegations of a ‘cover-up’ involving several arms of the State.