Another victim of the shootings died months later.
Following an extensive inquiry the UK Government apologised for the deaths which led to a PSNI investigation.
Police have now finished their interviews with former military personnel and are in the process of compiling a report for the PPS.
Detective Chief Inspector Ian Harrison, from Legacy Investigation Branch, said: "The families have been informed of this and we will continue to keep them updated in relation to developments.”
People Before Profit MLA Eamonn McCann called it a significant development.
Northern Ireland police launched their murder investigation in 2012.
The investigation came following the Government- commissioned inquiry led by Lord Saville which found that none of the victims were posing a threat to soldiers when they were shot.
The inquiry took 12 years to complete.
Prime Minister David Cameron apologised for the Army's actions following the publication of the report in 2010.
He branded them "unjustified and unjustifiable" and said he was "deeply sorry".
In September 2015 the PSNI told bereaved families they intended to interview a number of former soldiers about their involvement on the day, however, their progress has been thwarted by legal action.
Key findings of Lord Saville's report into Bloody Sunday
Lord Saville exonerated the victims of Bloody Sunday and delivered a damning account of the conduct of soldiers, concluding they had fired more than 100 rifle rounds on civil rights demonstrators without justification.
The Saville report's key findings were:
''The firing by soldiers of 1 Para caused the deaths of 13 people and injury to a similar number, none of whom was posing a threat of causing death or serious injury.'' This also applied to the 14th victim, who died later from injuries. The report added: ''We found no instances where it appeared to us that soldiers either were or might have been justified in firing."
''Despite the contrary evidence given by soldiers, we have concluded that none of them fired in response to attacks or threatened attacks by nail or petrol bombers.'' The report added that no one threw, or threatened to throw, nail or petrol bombs at soldiers.
The explanations given by soldiers were rejected, with a number said to have ''knowingly put forward false accounts''.
Members of the so-called Official IRA fired a shot at troops, but missed their target, though crucially it was concluded it was the paratroopers who shot first on Bloody Sunday.
The report recounts how some soldiers had their weapons cocked in contravention of guidelines, and that no warnings were issued by paratroopers who opened fire.
Speculation that unknown IRA gunmen had been wounded or killed by troops, and their bodies spirited away, was dismissed. There was no evidence to support it, and it would surely have come to light, the report said.
Northern Ireland Deputy First Minister Martin McGuinness, second in command of the Provisional IRA in Derry in 1972, was ''probably armed with a Thompson submachine gun'' at one point in the day, and though it is possible he fired the weapon, the report said that cannot be proved. But Lord Saville concluded: ''He did not engage in any activity that provided any of the soldiers with any justification for opening fire.''
Lord Saville concluded the commander of land forces in Northern Ireland, Major General Robert Ford, would have been aware that the Parachute Regiment had a reputation for using excessive force. But he would not have believed there was a risk of paratroopers firing unjustifiably.
The commanding officer of the paratroopers, Lieutenant Colonel Derek Wilford, disobeyed an order from a superior officer not to enter troops into the nationalist Bogside estate; while Lord Saville found his superior, Brigadier Patrick MacLellan, held no blame for the shootings since if he had known what Col Wilford was intending, he might well have called it off.
No blame was placed on the organisers of the march, the Northern Ireland Civil Rights Association.
Neither the UK nor Northern Ireland governments planned or foresaw the use of unnecessary lethal force.