Martin Gibbons, 52, was last seen on Thursday at around 5:30pm leaving Tameside General Hospital.
Martin is described as white, 5ft 4inches tall with a shaved head. He was last seen wearing a blue fleece, dark blue jeans, leather shoes and glasses.
Martin is known to frequent Manchester city centre and has relatives in Glossop.
Officers are becoming increasingly concerned for Martin and want to make sure he is safe and well.