Fr Tony Mullins was asked to oversee the running of the clerical affairs in Limerick since Dr Murray's resignation last month.
Fr Mullins is parish priest in Dromin-Athlacca, Co Limerick, and previously served as diocesan secretary as well as administrator at St John's Cathedral in the city.
He believes that it could be more than 12 months before a new bishop is appointed to Limerick.
"The last time we had a vacancy like this, where we didn't have any bishop, it took about 12 months. I'm just taking that as a guide.
"It could possibly be 12 months by the time this process of selection takes place. I would think it will be 12 months at least," Fr Mullins said.
"Rome is talking about reorganising the Irish Church. What that means and what impact it will have on Limerick, I don't know. However, it possibly could mean that we may have to wait longer than 12 months."
Dr Murray was the first Irish bishop to resign following the horrific revelations in the Murphy report.
The temporary administrator said the Catholic Church was in uncharted waters.
"Generally, the appointment of a bishop in the normal situation would be at least 10 to 12 months. But we are in a different situation now. It is a very unprecedented time for us."
Fr Mullins said he had not received any indication as to who the next Bishop of Limerick would be or where he would originate from.
"There is a process that the Vatican will put in place. I presume that will be sometime in the springtime when the (Papal) Nuncio takes soundings and so on from the priests of the diocese and others."
While Limerick waits for its next bishop to be appointed, Fr Mullins will continue to oversee the running of the diocese.
He said he had received "tremendous support" from his parishioners in Dromin-Athlacca, colleagues and friends since being appointed administrator to the diocese.
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