Ross Monaghan, 35, was shot in the back in a targeted attack at around 09:05 on Monday, 16 January.
He had dropped his child off at St George's Primary in Penilee when a man pushing an buggy pulled out a gun.
Police returned to the area one week on, to seek more information about the attack from parents of school children.
Between 25 and 30 uniformed and CID officers were outside the school and in Muirdykes Road between 08:00 and 09:00.
Det Ch Insp John Kennedy confirmed Mr Monaghan had left the country since the attack.
"We've briefly spoken to him but at this stage we have to re-interview him," he said.
"It's very difficult when he's in Spain at the moment."
Ross Monaghan was cleared of killing gangland figure Kevin "Gerbil" Carroll in 2012 after a judge ruled there was no case to answer due to insufficient evidence.
After the shooting, images of the man thought to be the gunman were published by the Scottish Sun newspaper.
The man, who can be seen pushing a buggy near the school, was wearing a blue padded jacket, blue jeans, a dark woollen bobble hat and a woollen scarf pulled up around his face.
The suspect is also believed to have been in the area, outside the school, on Friday 13 January 2017, with the buggy.
Det Ch Insp John Kennedy said detectives were trying to establish if anyone witnessed the gunman running with the buggy from the scene.
He said: "We don't think he went into a house in the Penilee estate.
"We're of the opinion that he left the area in a car, probably driven by another male."
Police investigating an attempted murder in Glasgow have been in contact with manufacturers of children's buggies from as far afield as China.