Samples of heroin were taken by gardaí after reports came back from a number of local drug workers that heroin users were complaining of high-strength heroin.
The samples were from the same batch of heroin which the two homeless men are suspected of taking.
The two men died in a period of four days in Cork city centre earlier this month, around the same time homeless man Jonathan Corrie died close to the Dáil.
The samples were sent to the State Forensic Science Laboratory for testing.
“There is nothing in the tests that is sinister; neither high strength nor contaminants,” said a Garda source.
The source pointed out that official figures show more than one person dies from drugs every day on average.
The Garda source said “unfortunately these things happen” with people living on the streets and using drugs.
He said it was often the case that such deaths involve heroin combined with other drugs, including tranquillisers like benzodiazepines.
However, he stressed that until toxicology reports came back from the two homeless men in Cork, they would not know what exactly was in their systems. He said the same was the case with Mr Corrie.
It comes as people in a Dublin community blighted by drug use for more than 30 years gathered last night for the annual lighting of a Christmas tree in memory of those who have lost their lives through drugs.
The ceremony, running for the last 18 years, took place at Buckingham St in the north inner city, beside a memorial marking drug deaths.
“It gives people an opportunity to remember their children and, in some cases, their mothers and fathers,” said Seani Lambe of Inner City Organisations Network.
“Christmas for anybody who lost a loved one is particularly poignant and it’s a recognition of their loss.”
Mr Burke, a veteran of drug campaigns since the early 1980s, said the drugs issue had “dropped off the agenda” and urged the Government to reappoint a junior minister with responsibility for the area.
“The Government needs to get the National Drugs Strategy back on track, because at the moment nothing seems to be happening. Drug projects have felt the full belt of austerity over the last four to five years.”
The National Drugs-Related Deaths Index shows there were 607 deaths in 2011, compared to 597 in 2010.