Peter Ball, the former Bishop of Lewes and Gloucester who boasted of links to royalty, has asked to join the Roman Catholic Diocese of Clifton, in Bristol, a spokesman for the Church confirmed.
His identical twin brother, the former bishop of Truro Michael Ball, also sent an email - seen by Press Association - to friends telling them of the idea.
Peter Ball, now 85, was jailed for 32 months in October 2015 for offences dating back to the 1970s against 18 young men at his home in East Sussex.
The email sent on Wednesday morning said the pair would not be sending Christmas cards after recent events had "totally wearied and reduced" them.
In it, Michael Ball said: "Peter and Michael will not be sending Christmas Cards this year.
"The events of the last years and rightly or wrongly the battering by the Church have totally wearied and reduced us.
"We will proabably [sic] be joining the Roman Catholic Church soon.
"We love The Church of England but would like to end our days in a church where we can live and worship in anonymity and without constant fear.
"We send our love and are enormously grateful fo [sic] the kindness and continued support of so many.
"We hope you have a wonderful Christmas and a joyful New Year."
The message was mistakenly sent to a BBC journalist and subsequently shown to Peter Saunders, the child abuse campaigner who founded support charity NAPAC.
Speaking to Press Association on Wednesday evening Mr Saunders, who sits on the Vatican's commission on protecting children from abuse, said: "It's not surprising they are moving to another church.
"If the Catholic hierarchy welcome him [Peter Ball] I hope they put in place every possible safeguard so that people know something about his background and he can never, ever pose a threat to children or young people again."
He said Michael Ball's complaint of taking a "battering" from the Church was "flippant" and it was "disgusting" the pair were acting as though they were the victims.
A spokesman for the Roman Catholic diocese of Arundel and Brighton said: "We confirm Peter Ball has been in contact with the Roman Catholic diocese of Clifton, in which diocese he now lives, expressing an interest in becoming a member of the Catholic Church.
"This matter is subject to discussions between Clifton diocese and the statutory authorities, who are the lead with regards to Peter Ball's risk management in the community.
"The Church of England authorities including their safeguarding team are aware of this request."
Neither Michael or Peter Ball could be contacted by Press Association.
But Michael Ball reportedly told the BBC a move to the Catholic Church was a "possibility".
Peter Ball's sentence came 22 years after the abuse first surfaced. He eventually admitted misconduct in a public office and two counts of indecent assault.
The court heard how Ball had convinced some of his victims to strip naked to pray and even suggested they submit to beatings between 1977 and 1992.
The first of his victims to come forward took his own life in 2012 after hearing Sussex Police had reopened the case.
Former Archbishop of Canterbury George Carey resigned as honorary assistant bishop in the Diocese of Oxford after the public inquiry into child sex abuse last year heard he delayed a "proper investigation" into Ball's crimes for two decades by failing to pass information to police.
A review of how Ball's case was handled found he used his connections to boost his position and was said to be a confidant of the Prince of Wales.
An independent review entitled an Abuse of Faith, led by Dame Moira Gibb, said he "betrayed his Church" and its followers.
The report added: "The Church at its most senior levels and over many years supported him unwisely and displayed little care for his victims."
Ball was released from jail in February after serving half his sentence behind bars.
