Known to pals as 'little Elvis', Mr Glennon lived in the flat while his partner, Debbie McEvoy, was a regular visitor.
That their bodies were discovered together has been described as fitting by those who knew them best.
Junior minister Joe Costello described the deaths as "tragic".
"I knew him well. He was the life and soul of the party and would get up and sing. He was at the Christmas party on Prussia Street and he was up singing.
"He would do anything for his neighbours and he was a real character. He loved company. He and Debbie were very close companions."
The pair may have been dead for up to four days before they were found by a care worker yesterday afternoon.
Friends and family of the couple have been left devastated by their deaths.
"John was a very jolly man. He was a great character and was very social. We called him Elvis because he always wore a cowboy hat and a tie with a guitar on it," said neighbour Tom Mullane.
Jimmy Traynor, who is married to Mr Glennon's sister Mary, said his death came as a shock.
He recalled that council officials were called to Mr Glennon's house over the weekend after he could not be contacted by phone.
However, when they gained entry to the house, Mr Glennon was fine.
Meanwhile a close friend of Ms McEvoy, Irene Daly, spoke fondly of the retired nurse who she said was a "quiet and dignified lady".
"Debbie was the loveliest person you could ever meet. She was extremely well educated and you would love to know her. She'd light up a room."
Ms McEvoy, originally from Newry, worked in the Rotunda and Beaumont hospitals.
Gardai are continuing to probe the deaths and post-mortem examinations were due to be carried out today.
While a gas leak was initially feared by investigators, it has since emerged that the apartment was heated by electricity.
Gardai now believe the OAPs may have died as a result of carbon monoxide poisoning. Carbon monoxide is a colourless odourless gas that can easily go unnoticed.
It is a by-product of burning fossil fuels and is often dubbed the 'silent killer'.
Minister Costello urged householders to take steps to protect themselves against carbon monoxide poisoning.
"People should ensure that all their household appliances are functioning properly and that their homes are safe and secure," he added.
His warning was echoed today by the chief executive of Natural Standards Authority of Ireland.
"Modern appliances burn very efficiently but there's a lot of power there, and if everything isn't set right there is the risk you'll get carbon monoxide.
"Modern homes are very well insulated, so if there's a build-up, it doesn't dispel as easily as it might in older homes," said CEO Maurice Buckley.
"You don't smell anything, you don't feel anything."