Missing Jason Goldrick may have been seen in Poulton a day after vanishing from Blackpool Victoria Hospital on November 1, it is understood.
The 50-year-old has still not been found, however, and the sighting has not been confirmed publicly by police.
Mr Goldrick, who has underlying health problems, is described as white, 5ft8ins tall, of a medium build, with short, grey hair. He was wearing a long sleeved dark blue jumper, dark blue joggers, and black trainers when he disappeared. Immediate sightings should be reported by calling 999.
A 47-year-old man from Blackpool was arrested on suspicion of murder by detectives last month, though they later released him under investigation and are again treating Mr Goldrick as missing.
Police have conceded, however, that “every day which goes by without finding Jason is more and more worrying”.
Officers searching for Mr Goldrick have been ordered to arrest him by magistrates in the resort, who put him on the wanted list after he missed a court appearance on Wednesday, November 27 – weeks after he vanished.