Mr Allen was shot dead on the night of February 9 2012 at the home of his partner in the outskirts of Buncrana, Co Donegal.
A father-of-two, the 24-year-old was originally from the Waterside area but moved to Donegal after he became the subject of threats in his home city.
Responsibility for his murder was subsequently claimed by dissident republican vigilante group, Republican Action Against Drugs (RAAD).
RAAD later merged with the then Real IRA to form the New IRA, one of the main dissident republican paramilitary organisations.
A claim by RAAD that Mr Allen was a drug dealer has been denied by both the dead man’s family and by Gardaí.
Mr Allen was shot through a door of the house at Links View Park in Buncrana and died at the scene despite his partner’s desperate efforts to save his life. It is believed three gunmen were involved in his murder.
In an appeal marking the eighth anniversary of the murder, Garda officer Detective Inspector Pat O’Donnell said officers believed they know who killed Mr Allen.
Mr O’Donnell said the organisation behind the murder was the same organisation that was responsible for the killing in Derry in April last year of journalist Lyra McKee.
The senior Garda officer said: “The people who murdered Andrew Allen are from Derry city.
“And it’s the people of Derry city I’m appealing to directly this morning to assist with the investigation because it’s the people who hold the key to solving this murder.”
A number of suspects have been arrested over Mr Allen’s murder but no one has yet been charged.