Willoughby, 32, is wanted on recall to prison after breaching his licence conditions.
He is described as white, 5ft 7ins tall, of a slim build with short, brown hair.
Willoughby has links to Parkgate in Rotherham, Balby in Doncaster and Driffield in the East Riding of Yorkshire.
Can you help? Please call 101 quoting crime reference number 420 of 1 February 2021.
Alternatively, you can stay completely anonymous by contacting the independent charity Crimestoppers via their website Crimestoppers-uk.org or by calling their UK Contact Centre on 0800 555 111.