The 49-year-old was shot dead outside his Ballyfermot home in the early hours of last Sunday morning.
Detectives are probing a number of lines of inquiry including whether Mr Tormey, described by locals as a “family man”, had a falling out with people involved in serious crime.
Yesterday gardaí made their first arrests in the case after armed officers detained a man and woman in west Dublin.
Independent.ie understands that they are known to Michael Tormey and are being quizzed on suspicion of direct involvement in the fatal shooting.
The man (40s) and woman (30s) are being held at separate garda stations under Section 50 of the Criminal Justice Act, 2007.
They can be held for up to seven days before they must either be charged or released from custody pending a file to the DPP.
Senior sources have described the arrests as “highly significant” and detectives have made major progress in the murder investigation.
Gardaí have officially said that Mr Tormey had no known involvement in criminality.
However, they are investigating if he fell out with serious criminals prior to his killing.
The arrests come as the dad's funeral is set to take place tomorrow.
He was shot at around 4.35am while standing in the driveway of his home at Thomond Drive in Ballyfermot.
His wife and six-year-old daughter were asleep in the house at the time he was killed.
It is understood nobody heard the shots despite Mr Tormey being hit a number of times.
He was found slumped on the driveway between the front door and a car, and a call was made to Dublin Fire Brigade who then alerted Gardaí after they attended the scene.
At a press conference this week Supt Tony Twomey, of Ballyfermot garda station, said around 20 officers are working on the investigation, with door-to-door enquiries being carried out in the area.
“We have a full investigation team assigned to this and we are happy that we will establish a motive within the fullness of time,” he said.
The senior officer said that Mr Tormey had attended a social gathering that night but they had ruled this out as being linked to his murder.
Gardaí are continuing to appeal for anyone with information in relation to the incident - in particular anyone who may have been in the Thomond Road, Landen Road, Kylemore Road or the general Decies area between 3:30am and 5:30am on the morning of Sunday, 9th January – to contact them.
Gardaí can be contacted at Ballyfermot Garda Station on 01 666 7200, the Garda Confidential Line on 1800 666 111or any Garda station.