"At this stage we are still investigating and considering charges in terms of the Animal Protection Act," Tshwane SPCA managing director Rick Allan said on Friday.
The NSPCA was looking into the manner in which the animal was transported.
"We believe the method in which the animal was transported was not correct. The death of the animal could have been avoided."
The giraffe died on Thursday after it hit its head while being transported, along with another giraffe, on a truck on the N1 in Centurion.
At the time, Allan said it died due to trauma to the head.
It was not clear what hit the giraffe's head.
"The head of the giraffe was above the vehicle."
Members of the public alerted the NSPCA about two giraffes being transported in a truck.