Three children were seen running away from the flat in a derelict block in Spey Road, on Sunday, April 22, at 3.30pm but no-one was injured. Fire fighters were alerted by neighbours and prevented the blaze spreading.
PC Andrew Frith said: "I would like to hear from anyone who noticed unusual activity around the area.
"I would also like to remind parents and guardians to ensure their children do not have access to cigarette lighters or any other items that can cause fire."
Anyone with information should contact PC Frith on the 24-hour non emergency police number, 101, call Crimestoppers anonymously on 0800 555 111 or visit crimestoppers-uk.org.