Mr Al-Essaie, 23, died in hospital after being shot in the chest in Daniel Hill, Walkley on Saturday 18 February.
South Yorkshire Police has not released any further details of those arrested.
Five people previously arrested in connection with the shooting have been released on bail.
Two more people have been arrested in connection with the fatal shooting of Assel Al-Essaie after armed police stopped a vehicle on the Sheffield Parkway.