The young man was pronounced dead at St James's Hospital last month, on December 1, following an incident in the south inner city.
Mr Heinrich, who was from Munich, was stabbed in the stomach outside his apartment in an attack in which his friend was also injured.
He lost a significant amount of blood at the scene and was rushed to hospital where he later died.
Gardai believe the two students were on a balcony at a party in the block of apartments when words were exchanged between them and two teenagers walking past.
Later when confronted on the street the teenagers produced knifes and the two German men were stabbed.
At the Coroner's Court, Detective Inspector Sean Campbell said he was seeking an adjournment of the inquest.
"A file is being prepared for the DPP and it is at an advanced stage," he told the coroner, Dr Brian Farrell.
He said that the family, who did not travel for the brief hearing from Germany, were aware that the inquest was being mentioned.
A deposition was read out from the victim's father, Wolfgang Heinrich, in which he said that on December 3, 2012, he identified the body of his son to Sergeant Paul Murphy of Kilmainham Garda Station.
It said that he was granting permission to the gardai to get his son's medical records.
Sgt Murphy told the court that he has been appointed as the family liaison officer.
He said that he identified the body of Thomas Heinrich to Professor Marie Cassidy, the State Pathologist.
Dr Farrell said that the cause of the death given by Professor Cassidy was "stab wounds to the abdomen".
He asked Sgt Murphy to convey sympathies to the family back in Germany.
Dr Farrell said that a death certificate would be made available.
The court heard that Thomas was the only child of Wolfgang and Alexandra Heinrich.
Wolfgang has children from a previous marriage.
Thomas was one of around 50 German students from the MHMK media college in Munich spending a foreign semester in Dublin.
He had been attending Griffith College. The student had been due to return home permanently to Germany three weeks after the fatal stabbing when his study period in Dublin came to an end.
The inquest was adjourned until a date in June.
Meanwhile, a separate inquest into the death of Dubliner Shane O'Connor, who died on the October 29 last year from a stab wound to the chest, was adjourned on Friday at the coroner's court.
Gardai, who are conducting a homicide investigation, made an application for the inquest to be adjourned.
The 22-year-old, of St Donagh's Road, Donaghmede, was pronounced dead at Beaumont Hospital in the capital, the Coroner's Court heard.
Dr Farrell said that he would adjourn the inquest until June as the investigation was ongoing.