The Very Reverend Dr Jeffrey John, Dean of St Albans, said that the only reason he was denied the position was because some members of the Electoral College did not want to deal with the controversy of appointing a gay bishop.
In a letter to the Bishop of Swansea and Brecon, Rt Rev John Davies, he wrote that during the selection process, some members of the Electoral College alleged that a number of homophobic remarks were made and "left unchecked" by the chair.
Dr John added: "...the only arguments adduced against my appointment - in particular by two of the bishops - were directly related to my homosexuality and/or civil partnership - namely that my appointment would bring unwelcome and unsettling publicity to the diocese, and that it might create difficulties for the future Archbishop in relation to the Anglican Communion."
The Dean of St Albans allegedly received more than half of the votes in the Electoral College vote but did not receive the two-thirds majority required.
He was told on Friday that he would not receive further consideration in the process.
Rev Peter Ould, an Anglican priest and commentator on Church issues told Premier News Hour that the situation is messy.
"It looks as though from all the leaks and so on that pretty much all the representatives from Llandaff wanted Jeffrey John but he was blocked by some of the other members of the deciding committee so I can understand why Dr John at this point will feel very frustrated," Rev Peter said.
Church in Wales rules state that because the Electoral College could not come to a decision on a new bishop, the decision is now taken out of their hands and given solely to the five remaining diocese bishops in Wales to make the choice themselves.
A Church in Wales spokesperson told Premier: "The appointment process is still ongoing and is confidential.
"However, I can say that under the rules of our constitution, a candidate has to have two-thirds of the votes of the Electoral College in order to be elected as bishop.
"In the case of the recent Llandaff election, no candidate secured enough votes to be elected.
"Neither homosexuality nor participation in a civil partnership are a bar to any candidate being either nominated or elected as a Bishop in the Church in Wales and this was made clear to members of the Llandaff Electoral College by its President, the Bishop of Swansea and Brecon, at its meeting last month."
Jeffrey John entered into a civil partnership with Grant Holmes in 2006 after a 30 year relationship. They have stated their relationship is celibate.
In 2003, Dr John was nominated as Bishop of Reading but stood aside after Dr Rowan Williams asked him to withdraw from the process in order to avoid a church split.