Members of the Electoral College had been locked inside the diocese cathedral to try and find a replacement for former Archbishop Dr Barry Morgan.
But the Church in Wales said they had failed to agree on a name.
One person who was thought to be in the frame was Jeffrey John - an openly gay clergyman. He would have needed two thirds of the 47 members to give him their support.
Candidates for election are nominated at the meeting and voted on by ballot. Any candidate receiving two-thirds of the votes of those present is declared Bishop-Elect. Otherwise, the College returns to the nomination stage and the cycle starts afresh.
Because the college failed to elect a bishop the responsibility of filling the vacancy falls to the Bench of Bishops.
The Bishop of Swansea and Brecon, John Davies, who is President of the Electoral College, said the process leading up to an eventual appointment would include a wide-ranging consultation of both the laity and the clergy from across the Church in Wales.
The nomination will not automatically be appointed archbishop of the church, however he or she will be in the running along with the five other bishops.