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Nine people, including an eight-year-old girl, were killed in the village of Claudy in one of the most controversial incidents of the Troubles.
There was an alleged deal between the UK government and the Catholic Church not to arrest Father James Chesney.
Fr Chesney was moved across the Irish border by the Church after the attack.
The priest, who died in 1980, had been the curate in Cullion, a small parish in County Londonderry.
No-one convicted
The Bishop of Derry, Neil Farren, responding to rumours that Fr Chesney was a member of the South Derry Brigade of the IRA and may have been involved in the bombings, called him in for questioning.
In 2002, Bishop Farren's successor, Edward Daly, told the BBC that Fr Chesney had denied any involvement with the IRA "utterly, unequivocally, vehemently".
However, he did tell his superiors that he had "republican sympathies, very strong republican sympathies".
The Ombudsman, Al Hutchinson, has been examining the original RUC investigation.
No-one has ever been convicted of the bomb attack in which both Protestants and Catholics were killed.
The youngest victim was eight-year-old Kathryn Eakin who was cleaning the windows of the family grocery store when the first bomb exploded.
The other people killed were Joseph McCluskey, 39; David Miller, 60; James McClelland, 65; William Temple, 16; Elizabeth McElhinney, 59; Rose McLaughlin, 51; Patrick Connolly, 15; and Arthur Hone, 38.
As well as the power to investigate complaints against the Police Service of Northern Ireland, the Police Ombudsman also has the authority to probe investigations carried out by the predecessor to the PSNI, the RUC.
More general investigations into incidents during the Troubles are handled by a dedicated group of PSNI detectives - the Historical Enquiries Team.
'Bring justice'
BBC Ireland correspondent Mark Simpson said the report "is expected to confirm that the authorities at the time were aware of the suspected involvement of a priest in the atrocity - but failed to arrest him".
"Instead, a secret deal was done between the Catholic Church and the state to move Fr Jim Chesney across the border into County Donegal," our correspondent added.
"The rumour which has been swirling around the County Londonderry village for the past 38 years is there was no justice for the nine people killed, simply a cover-up.
"If the Ombudsman's report substantiates it, there will be questions for the Catholic Church to answer."
Speaking in 2002 shortly after the investigation reopened, Merle Eakin, the mother of Kathryn Eakin, said: "We are just hopeful that they will bring justice and the people who are still alive will be brought to justice - that is what we really want."
In 2005, four people, including a Sinn Fein Assembly member, were arrested in connection with the bombing.
They were released without charge a few days later, with Sinn Fein's Martin McGuinness calling it a political stunt.
This is the official PSNI report.