West Yorkshire Police are seeking information on the whereabouts of Nathan Joblin, but say member of the public should not approach him.
The 20-year-old was last seen in the Middleton area of the city at around 11am.
A police spokesman said: "He is considered extremely vulnerable and police are very concerned for Nathan’s welfare.
"Anyone who sees Nathan is asked not to approach him, but to immediately report any sightings to the police."
Nathan is described white, around 5ft 9in and slim. He has short light brown hair and was last seen a dark coloured Bench jacket and black tracksuit bottoms.
He was carrying a brown hessian bag in his hand and a small black coloured bag over his shoulder.
Anyone who has seen Nathan or who knows where he is now is asked to contact police via 101, quoting log 636 of December 14.