Mark James Smith, 41, was last seen at the Asda on Kirkstall Road at around 8.40am on Thursday, October 14.
When last seen, he was wearing blue jeans, a black jacket and black cap.
He was with his Staffordshire bull terrier.
Records show that he purchased a tent and it is possible he is camping in the local area.
Officers are concerns for his welfare and want to trace him.
Anyone who has seen Mark Smith is asked to contact police by calling 101 or using 101 Live Chat on the West Yorkshire Police website, quoting log 1092 of 14/10.