Mark Chung, who officers have advised the public not to approach, was reported missing from Castle Huntly at 10:00 on 3 October.
Police described him as being of Asian appearance and speaking with a Merseyside accent.
They said he was known to have connections in both Glasgow and Merseyside.
Chung is described as being 5ft 9in tall, of stocky build and has a shaved head.
When last seen he was wearing glasses, a grey sweatshirt, grey jogging bottoms and black and grey trainers.
Police have issued a renewed appeal to trace a man who absconded from an open jail near Dundee two weeks ago.