Filin told the BBC he would not name names until police have made an announcement about their investigation.
"I not only have a suspicion about who did this, but I'm absolutely certain I know who did this. But I will only speak about this when investigators are ready to announce this," he said.
Filin, 43, suffered third-degree burns to his face and eyes when he was attacked Jan. 17 while he was walking home.
No arrests had been made and a motive was unknown but investigators said they suspect it could be traced to internal theater politics.
Filin said he had already undergone five surgeries to repair his face and attempt to restore sight to his eyes. He is scheduled to travel to Germany for another procedure, the BBC reported Sunday.
"My eyes are being monitored constantly. One eye was more damaged than the other. The left eye was damaged a little less, the right eye was damaged more," he said. "Based on what I feel, when the doctors give me the opportunity to sort of open my eyes and try to see something, I think that there's a chance that I will be able to see my children again. I really want to believe that."