Yesterday detectives staged a reconstruction of the crime as officers wearing similar clothing to the two killers retraced their getaway route in the hope that people in the community will come forward with information.
Mr Reilly was shot twice in the chest in the living room of his home, while two other people in the house were forced to lie on the kitchen floor.
Despite the efforts of paramedics, he died at the scene. His funeral took place on Wednesday.
The officer leading the investigation, Detective Chief Inspector Peter Montgomery, said: "We are following a number of definite lines of enquiry as part of this investigation.
"We believe the murder may be linked to illegal drugs and that it may have been carried out as some form of paramilitary-style shooting.
"We are still in the early stages of this investigation. Some progress has been made but we need more assistance from the community.
"Thanks to the response to our appeal last week we now have a clearer picture of where the killers went after the murder."
The detective said that to find Mr Reilly's murderers, they need answers to a range of questions.
"We need to know what happened next: did they get into a car or did they continue on foot along to the Belle Steel Road or cross the Pantridge Road into Colin Mill?
"We are also interested in confirming how they arrived at Joe Reilly's house: did they walk there or were they dropped off from a vehicle nearby?
"Both were wearing half-zip hooded sports tops and skin tight jogging bottoms. Both had their faces covered and at least one had a Celtic scarf up over his face and was wearing dark-rimmed glasses.
"We need to know where these men came from before the shooting, where they went afterwards and we want to speak to anyone who recognises the clothing."
DCI Montgomery added that Mr Reilly's family are devastated at his death and have asked to be allowed to grieve in private.
Anyone with information about the murder is asked to contact detectives at Musgrave police station on the non-emergency number 101 or to phone Crimestoppers anonymously on 0800 555 111.