UPDATED: North Yorkshire Police confirmed on Sunday that a 14-year-old boy has been arrested in connection with the fire.
The blaze at Overdale School, which has been closed since July 2021, broke out at around 8.30pm on Friday on Hawthorn Walk in Eastfield.
Eastfield residents have helped to identify the suspects who are thought to have deliberately started the blaze when they posted a photograph of a group of teenagers in the grounds shortly before it began on a community Facebook page.
North Yorkshire Police have issued descriptions of the three boys they are seeking: "All three are teenage boys. The first is described as thin, white, around 15 years old and had a bowl haircut. He was wearing a black jacket with white panels across it and black tracksuit trousers.
"The second is described as looking around 13 years old, white, chubby, with a black jacket, blue hoodie and grey jogging trousers.
"We are still working to get a description of the third suspect. We are still making enquiries at the scene and this incident is being treated as arson.
"Anyone with information should call us immediately on 101, select option 1 to speak to the Force Control Room and quote incident number 459 of today."
Since its closure Overdale has been replaced with a new community primary school built on a site nearby.
Firefighters from stations across the region were working until the early hours of Saturday morning to extinguish the flames.
Scarborough News photographer Richard Ponter was at the scene this morning and has captured images of the aftermath.