They ave also released descriptions of two men seen leaving the area.
The murder bid is being linked to the murder in May last year of IRA chief Gerard ‘Jock’ Davison in the Markets district.
Investigating officer, Detective Inspector Pete Mullan said: “ We believe two men called to a house at Distillery Court at 9.45am on Friday morning and shot the victim a number of times inside the property.
“The attackers then made off on foot towards the Grosvenor Road.
“The victim was able to raise the alarm with neighbours and an ambulance arrived to take him to hospital. He is currently in a stable condition in hospital.”
“We are continuing to work to establish the full circumstances surrounding this incident and the motive behind it.
“We have received reports of two men leaving the scene immediately after the shooting and descriptions of them.
“Both were described as being slightly under 6’ tall and both were wearing cycling shorts or leggings.
“They also both wore long sleeved yellow hi-vis tops, dark hats, black masks over their faces and dark gloves. One of the men was also carrying a dark coloured rucksack.
“I am appealing to anyone who saw two men matching these descriptions in the Distillery Court/ Grosvenor Road area on Friday morning at the time of the shooting, or anyone who has any information which may be of assistance to our investigation into this brutal attack, to contact detectives at Musgrave on 101.
“Alternatively, callers who do not wish to provide their details can contact the independent charity Crimestoppers on 0800 555 111.”