Fr Michael Seed, who is known for bringing high-profile politicians and aristocrats into the Catholic fold, made the prediction to friends at a recent memorial service, Times Online reports.
According to the paper, when contacted Fr Seed did not deny his comments, but said he did not know if Mr Blair would ever be received "formally" into the Roman Catholic Church.
To do so he would have to take part in a ceremony called the rite of Christian initiation for adults, followed by confirmation and taking the sacrament of Holy Communion.
Father Seed said: "He's been going to Mass every Sunday. He goes on his own when he is abroad, not just when he is with his wife and children."
Another church source said that many of the early saints and martyrs were not baptised. Such people were held to have had a "baptism of desire".
He said that Mr Blair was a Catholic by desire and that this did not necessitate a formal conversion. "He is an ecumenical Catholic," said the source. "He is a liberal Catholic. In terms of his private life, he is a Roman Catholic."
Although technically an Anglican, Mr Blair only "darkened the door" of Anglican churches on state and other formal occasions, he added.
Downing Street would not comment on the suggestion that Mr Blair would declare himself a Catholic. A spokesman said: "This story is always circulating in one form or another. The PM remains a member of the Church of England."
Blair will be welcomed into Catholic fold via his 'baptism of desire' (Times Online, 17/5/07)
Could Blair be on the verge of declaring himself a Catholic? (This is London, 17/5/07)
LINKS (not necessarily endorsed by Church Resources)
Tony Blair (Wikipedia)
Catholics, Protestants share power in N Ireland (CathNews, 9/5/07)
Westminster Cardinal and Blair in condom clash (CathNews, 4/12/07)
Pope appeals to Blair against Iraq war (CathNews, 24/2/03)
18 May 2007