Lee Smith, aged 39, was reported missing shortly before 4pm yesterday (September 18) after he left his home in Harehills in the morning.
He was then seen in the Armley area last night.
Leeds District CID (criminal investigation department) have issued an appeal for information.
A police spokesperson said: "There are genuine concerns for his welfare and officers are currently making enquiries to trace him to check that he is safe."
Mr Smith is described as white, 5ft 10ins tall, of stocky build and clean-shaven with mousy brown hair.
He was last seen wearing a navy top and grey tracksuit bottoms.
Anyone who has seen him or who has any information can contact Leeds District CID via 101 quoting log number 1107 of September 18.
Officers are also appealing directly to Mr Smith to contact them to let them know he is safe.
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