Officers say the man was last seen in Bedford Street in Stockton at about 3.30pm yesterday (May 30), when he told people his name was Andy.
He is described as a white man, about 50 years of age, very messy hair wearing a dark grey thin jacket, tracksuit bottoms and a distinctive green backpack.
The man left the area before officers arrived and is believed to be heading in the direction of Mellor Street and possibly onto Durham Road.
Officers have been searching the area but have not yet been able to locate him and are appealing to anyone who thinks they may have seen him to come forward.
A spokesperson from Cleveland Police said: “We would like to find the man to make sure he is okay and offer any necessary support to ensure his safety and welfare.”
Anyone who thinks they might have seen the man is asked to contact Cleveland Police on 101.