The UK Daily Mail reports that Mr Blair has discussed becoming a Roman Catholic deacon when he quits office.
The "revelation" comes as he prepares to meet the Pope amid speculation that he will use the audience in the Vatican to announce his conversion.
In his last foreign engagement, just days before he leaves Downing Street for the final time, the Prime Minister will visit Pope Benedict XVI in what officials say will be a "highly significant" personal mission.
It is thought that Tony Blair will announce his conversion to Catholicism when he meets the Pope, the paper says.
Reports that he will convert from the Church of England to the Catholic faith of his wife Cherie have often surfaced during Mr Blair's decade in office.
The claims were supported by revelations that he has already discussed not only converting to Rome, but also taking a formal position within the Church.
Mr Blair discussed the idea of his taking such a role with Canon Timothy Russ, priest at the Immaculate Heart of Mary near the Prime Minister's official country residence, Chequers.
The revelation is contained in a new book soon to be serialised by The Mail on Sunday - The Darlings Of Downing Street by Garry O'Connor.
The book states: "Tony expressed his strong desire when he stepped down to become a deacon - and a Roman Catholic deacon at that, confirming the often-speculated belief that he would convert to Roman Catholicism sometime in the future."
Mr Blair is reported as asking his confidant Fr Timothy: "Would this be possible?" He was told: "It usually takes two or three years", to which he replied: "The fact that I'm PM, could this make a difference?"
The deacon idea emerged in a conversation a few years ago about Mr Blair's plans after he leaves office.
Fr Timothy suggested that taking on a formal role in the Church could give him fresh moral clout when he campaigns on climate change and Africa.
The priest added: "He has a lot of potentiality for good. He is still looking for the meaning in his life."
Blair 'may become a Catholic deacon' (Daily Mail, 11/6/07)
LINKS (not necessarily endorsed by Church Resources)
Immaculate Heart of Mary Roman Catholic Church, Great Missenden
Tony Blair (Wikipedia)
British PM to become a Catholic, family priest hints (CathNews, 18/5/07)
Westminster Cardinal and Blair in condom clash (CathNews, 4/12/07)
Pope appeals to Blair against Iraq war (CathNews, 24/2/03)
12 Jun 2007