A gun was fired at a car parked outside the Co-op on Chapel Street, Woodhouse, on Monday night.
Three men jumped into the car and sped off, with South Yorkshire Police investigating the possibility that there was somebody in the vehicle at the time.
Last night, the potential victim had still not been identified.
Temporary Detective Chief Inspector Jamie Henderson, leading the police probe, said: “Our efforts to identify and trace who was in the car at the time of the incident continues, as it’s vital we ensure their safety.”
But South Yorkshire Police said members of the public could have also been shot in the incident.
“The incident occurred in a car park of a convenience store, where people were shopping and going about their daily businesses and there were lots of witnesses,” the force said.
“Someone could’ve clearly been caught in the crossfire but thankfully, we don’t believe this to be the case.
“We haven’t got people coming forward to speak to us or identify themselves as a victim or that they were injured in the incident.”
Last night, six people remained in custody after being arrested on suspicion of possession of a firearm with intent to cause fear or violence.
Anyone with information should call South Yorkshire Police on 101 or Crimestoppers, anonymously, on 0800 555111.
Quote incident number 843 of September 30.