The Vatican is expected to appoint an assistant bishop to the Archdiocese of Armagh, working under Cardinal Sean Brady.
The Irish Catholic newspaper described the move as an "exit strategy" for Cardinal Brady.
Last May, the head of the Catholic Church in Ireland, 73, said he would not resign despite revelations about his handling of clerical abuse claims.
There has been speculation that the new role will be given to Monsignor Eamon Martin, the current diocesan administrator of the Diocese of Derry.
However, there has been no official confirmation as yet.
The editor of The Irish Catholic, Michael Kelly, told the BBC the identity of the coadjutor bishop was a well-guarded secret.
"Normally these things would be an open secret in some way," he said. "Even senior Irish bishops were only told on Thursday night that the Vatican will on Friday morning at 11:00 GMT Irish time appoint a coadjutor bishop."
"This is an exit strategy for Cardinal Brady and probably something where this new shadow bishop will take over within the next three or four months.
"It's been very clear that the cardinal's position has been, to say the least, difficult in the church and the Vatican has been engaged in a search for a search for his successor. It seems now they have eventually found a successor who will shadow the cardinal, allowing the cardinal, at least on paper, or at least publicly, to go at a time of his own choosing."
A BBC documentary found that when Cardinal Brady was a priest, he had names and addresses of those being abused by paedophile priest Brendan Smyth, but did not pass them to police or parents.