Paula Vennells, who lead the Post Office during the Horizon scandal, was on the final three person shortlist to become Bishop of London in 2017.
According to the BBC she was interviewed for the role before it was given to Dame Sarah Mullally.
In a statement,a spokesperson for the Church of England said: "We never make any comment on who is a candidate, or not, in what is a confidential discernment process."
The revelation comes on the day Vennells announced she was handing back her CBE in light of her role in the Horizon scandal which saw hundreds of subpostmasters being wrongfully prosecuted.
Their pleas that the IT system was faulty fell on deaf ears at the time, and many were convicted of fraud with some being fined or sentenced to time in prison.
Vennells denied there was a problem, and was awarded a CBE in December 2018.
But a recent TV dramatisation of the story has brought the widespread miscarriage of justice back into the spotlight, and intensified claims for her to hand back the honour. More than a million people signed a petition calling for it to be revoked, and the Prime Minister Rishi Sunak said on Monday that he would 'strongly support' moves to look into that as a possibility.
In a statement Ms Vennells said: "I continue to support and focus on co-operating with the Inquiry and expect to be giving evidence in the coming months.
"I have so far maintained my silence as I considered it inappropriate to comment publicly while the Inquiry remains ongoing and before I have provided my oral evidence.
"I am, however, aware of the calls from subpostmasters and others to return my CBE.
"I have listened and I confirm that I return my CBE with immediate effect.
"I am truly sorry for the devastation caused to the sub-postmasters and their families, whose lives were torn apart by being wrongly accused and wrongly prosecuted as a result of the Horizon system.
"I now intend to continue to focus on assisting the Inquiry and will not make any further public comment until it has concluded."
Ms Vennells, who was CEO of the company from 2012 to 2019, after it split from Royal Mail turned the loss-making company into a profitable one. The installation of the Horizon software predated her time at the company, and she has previously said she was given wrong information and was led to believe the local managers were the ones at fault.
She trained for ministry in Oxford, and served as a non-stipendiary (unpaid) minister in the Diocese of St Albans. She was reported to have 'stepped back' from duties in 2021, but is being offered support from the church congregation.
The Bishop of St Albans, himself the son of a sub-post master said: “The recent ITV dramatisation understandably rekindles the suffering and pain of the sub-postmasters and their families who are victims of the Horizon IT scandal, and anger in all of us for such a serious miscarriage of justice.
“I hope and pray that the public inquiry will explain fully the sequence of events, provide redress for the victims and hold to account the responsible people and organisations.”
In a statement three years ago, the Rt Rev Alan Smith said he had maintained a "close watch" on developments and that "no culpability was attributed to any specific individuals".
