Spokeswoman Marcie Moriarty says they will not name the suspect in the case until Crown prosecution decides if it will lay charges.
The dog's owner Brian Whitlock was questioned about the matter by police earlier this week after he was arrested on unrelated charges of criminal harassment.
Whitlock was released from custody on his own recognizance Thursday, leaving the B.C. Provincial Court in the Downtown Eastside by a side door.
Investigators with the SPCA say the dog was emaciated and badly injured when it was discovered wrapped in blood-soaked blankets in a Kitsilano dumpster. Despite their attempts to save the dog, Captain died from his injuries last week.
Earlier this week CBC News obtained a copy of information sworn out to obtain a search warrant regarding the dog's death.
In it, a witness told the B.C. SPCA he'll be haunted by the sound of banging coming from Whitlock's apartment on July 18, the day neighbours found the gravely wounded dog in a dumpster behind the apartment building.
Wednesday night, hundreds of people and their dogs gathered at Vancouver's Kits Beach to mark Captain's death.