David Butterworth, a patient on The Harbour's acute mental health ward, climbed over a garden wall at the facility in Preston New Road on Wednesday, December 20.
The 60-year-old was later reported as missing and was last seen in the Preston New Road area, close to The Harbour, at 5.52pm that day.
He has not been seen or heard from since.
If you believe you saw David on or after December 20, captured him on dashcam/CCTV or have any information that could help police find him, call 101 or email forcecontrolroom@lancashire.police.uk quoting 1284 of December 20.
Call 999 for immediate sightings.