Its bishops have been meeting for three days to discuss the appointment, after a previous attempt to agree a name failed.
It followed the retirement of Dr Barry Morgan at the end of January.
The panel of Welsh bishops said they hoped to make a decision "as soon as all necessary formalities are finalised".
Last month, an electoral college of 47 people, including the Welsh bishops, met to vote for a replacement to lead the diocese from the Cardiff cathedral.
But none of the candidates received the required two-thirds majority support needed.
It means the appointment will now be made by the Church in Wales Bench of Bishops.
The Bishop of Swansea and Brecon, John Davies, who is the senior bishop, thanked everyone following a fresh consultation on the appointment.
"We received a wide variety of responses to the consultation and heard from a particularly large number of people suggesting possible candidates," he said.
"We have now considered those responses and, after a lengthy but productive meeting, we are ready to move to the next stage in the appointment process."
Church officials said there was no fixed timetable for the decision to be made but bishops wanted to make the appointment as soon as possible.
A new shortlist of candidates to become the next Bishop of Llandaff has been drawn up, the Church in Wales has said.