However, he confirmed they had narrowed down a list of more than 10 suspects.
"We have narrowed that down to one who we think is the most likely offender."
Mr Cook said the police station had been "flooded" with information about the case.
Paw Justice has offered a $2000 reward for information leading to the prosecution of the offender. However, Mr Cook said police had been contacted by numerous callers not seeking a reward.
"It's not all down to the reward. It is more public concern regarding animal cruelty. Any normal person would think this is unacceptable."
Marie Aitken, who owns the tortured cat Midnight, said she had received tip-offs through Facebook, and had heard that the culprits were "bragging with friends about how they tortured cats over the weekend".
She was glad to hear that someone would be arrested.
"It will help me sleep now."
However, she was still angry about what had happened and said the family was considering moving away from the area.
"It is pretty disturbing that the community would let someone like that live here. It's scary, there are kids around here."
She did not know the suspected offender but understood that they lived nearby.
Midnight was due to return home after having had ear surgery and was starting to return to normal, Mrs Aitken said.
"She's is jumping up and down."
Mrs Aitken was grateful for all the support that people had shown and the donations that had been made. The SPCA was paying the vet's bill and had been accepting donations.
Dixon House residents were so upset by what happened to the cat they got together and donated $50. Mrs Aitken said once Midnight was feeling better she would take it to visit the rest home.
- Greymouth Star