The 37-year-old Ford Transit driver was not injured in the incident in Neilston Avenue in the Priesthill area of Glasgow last Tuesday evening.
A Volkswagen Passat was spotted at the scene and was later found burned out near Rouken Glen Golf Club.
Police said it was stolen in August last year. Forensic teams have been working on the car and a number of items have been recovered for further examination.
Officers have been checking CCTV from the area and returned to the scene of the shooting and the entrance to the golf club to speak to anyone who may have been in the area at the same time last week.
The investigation has so far found that a 4x4 vehicle was seen driving off from near the golf club shortly after the Passat was set alight.
Officers want to trace the car, which is thought to be silver, white or cream.
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Detective Inspector Greg Wilkie said: “We are still trying to establish a motive for this incident and we’re very keen to speak to the occupants of the 4x4 vehicle seen driving off minutes after the Passat was set alight.
“The purpose of the operation is to gather further information, perhaps jogging someone’s memory which will enable officers to obtain further detail which could assist the investigation.”
Anyone with information can contact police on 101, or anonymously via Crimestoppers on 0800 555 111.