Ross Monaghan, 35, was shot in the back in a targeted attack outside St George’s Primary in the Penilee area of the city at about 9:05am on 16 January.
He was approached by a man pushing an empty buggy who pulled out a gun and fired at him before fleeing along Hollybush Road.
Police Scotland launched a major investigation and Crimestoppers is now offering a reward for information that leads to a conviction.
Mr Monaghan was cleared of killing gangland figure Kevin Carroll in 2012 after a judge ruled there was no case to answer due to insufficient evidence.
Following the incident outside the school, Mr Monaghan left hospital after brief treatment and is reported to have now left the country.
Angela Parker, national manager of Crimestoppers in Scotland, said: “It’s shocking to think that this attempted murder happened right in front of a busy primary school in broad daylight at the start of the school day.
“The parents of the school and the nearby Penilee estate have a right to feel safe, especially when they are dropping off children in front of the school .
“We are now offering a substantial reward for information given to Crimestoppers and urge local people or anyone who is in the know to please pick up the phone or log on to our website and pass on information in compete anonymity.”
The gunman was wearing a blue padded jacket, blue jeans, a woollen scarf pulled up to cover his face and a dark woollen bobble hat.
Last week, Detective Chief Inspector John Kennedy said some people were fearful of coming forward with information.
He said: “This is a difficult type of investigation to get people to come forward and that’s why I would suggest if they are fearful of approaching the police here, they can contact us outwith this environment or through Crimestoppers.
“Parents are still concerned but by the police presence and the intensity of our investigation, we’re hoping that we’re reassuring them.”