Jan Briggs, 63, was last seen on November 17 at 9.30pm.
Police believe he is residing in the Headingley area of the city, but he has still not been found almost four weeks after going missing.
He is described as having short, dark grey hair.
Mr Briggs is believed to have been wearing glasses, a dark blue Regatta hooded-waterproof jacket, grey trousers, a grey fleece and black shoes.
Anyone with information is asked to call police on 101, quoting log 966 of November 18.