Stephen Pollock, 21, was found dead at a friend’s house in Weaver Terrace, Paisley, at around 11.15pm on December 21.
Officers investigating the shooting found a firearm near the scene last night.
This evening, a week on from the murder, police will stop and interview motorists and pedestrians in Cathcart Crescent, Paisley, in a bid to jog their memories.
Detective Superintendent Alan Buchanan said: “A team of officers is currently working around the clock on this inquiry in an attempt to identify the person responsible for this terrible crime.
“Last night, officers recovered a firearm which we believe may be linked to the investigation near to Weaver Terrace, Paisley.
“We are still working to gather as much information on Stephen in order to try and find out the motive for this murder.
“Stephen had a lot of friends and was regularly seen walking his golden retriever dog in the Hunterhill area.”
Mr Pollock, who worked at Sandyford abattoir in Paisley, was last seen alive at his family’s home, around 10 minutes walk from the scene, at about 3.30pm on December 21.
Police are trying to piece together where he was in the hours between.
Last week his mother Nancy appealed for information which could help catch whoever is responsible for her son’s death.
She said: “Stephen was a great son and much loved by all the family.
“Our lives will never be the same and we will never get over not only losing Stephen, but losing him in such a horrific and tragic way - no family should ever have to put up with what we have suffered.”
Police said that extra uniform officers will maintain a presence in the Weaver Terrace area to reassure the public.