They struck Awan Foodmarket and Newsagents in Buchanan Road, Parson Cross, at 4am on Tuesday.
South Yorkshire Police said the raiders failed to gain entry.
Just over an hour later, ram raiders also attempted to gain entry to the Co-op on High Street, Ecclesfield.
Again, a vehicle was driven into the shutters but entry to the shop was not gained.
South Yorkshire Police have not disclosed whether the incidents are being linked.
Anyone with information should call South Yorkshire Police on 101.