The man who died in the incident at a housing estate in Tymon Road North in Tallaght has been named locally as Dan Reilly, the Irish Times reports.
At least four shots were fired at a house in Tallaght in the early hours of Monday morning shortly before Mr Reilly was fatally injured in a suspected hit-and-run.
Gardaí suspect the van was being driven by a man known to the deceased.
A file will be prepared for the Director of Public Prosecutions and gardaí at Tallaght are continuing to appeal for any witnesses to the incident to come forward.
Gardaí said on Tuesday that they are particularly interested in a dark coloured hatchback car that was seen leaving the area around the time of these incidents.
Gardaí are also appealing for anyone with camera footage, including dash-cam, to come forward.
