Local sources have named the injured man as Ross Craig, who, it is believed, had previously fled Scotland for Cyprus in 2006 after a city centre assault in which two men received knife wounds.
The 28-year-old was said to have been on bail when he attacked the men. He was arrested on his return from Cyprus, and in 2010 was sentenced to six-and-a-half years.
Detectives are appealing to the public for information following the incident at Shawhill Road on Thursday, March 9.
Around 8.10am, Craig was getting into his vehicle when he noticed another male standing at the bottom of his driveway. After going to investigate, he was then shot once in the leg.
The victim then chased the suspect down Shawhill Road, turning right into Hector Road and towards Pollokshaws Road. He continued to follow him into St Ronan’s Drive, where a dark coloured vehicle was waiting. The suspect entered the car which then drove off turning right into either Woodstock or Peveril Avenue.
The shooter is described as 5ft 7” in height, wearing dark clothing and a dark beanie hat.
Detective Inspector Colin Hailstones, Cathcart CID, said: “We now understand that the incident occurred around 8am this morning in a highly-residential street in the Shawlands area.
“The 34 year-old man was shot once and he received injuries to his leg and has been treated in hospital. He has since been released.
“I know that local residents will be concerned by this incident. We understand that this was a targeted and isolated attack. It is being treated as attempted murder.
“Detectives are currently searching the area around Shawhill Road, Pollokshaws Road and St Ronan’s Drive. Specialist officers will be conducting work in the area alongside detectives and we are conducting door to door enquiries and assessing opportunities to capture CCTV.
“We will not allow such a brazen act of violence to go unaccounted for. Please contact us with any information or contact Crimestoppers on 0800 555 111, where information can be given anonymously.”
Area Commander for Glasgow South East, Chief Inspector Hilary Sloan, said: “I completely understand that people will be concerned by this incident and we will have an increased uniformed presence in the area. I would ask local residents to approach those officers with any information or concerns that they have. You may have heard a disturbance, witnessed the chase or heard a car speeding off.”
Anyone with information is asked to contact the police at the Cathcart office on 101.