Craig Moverley, aged 46, from Inverness, Scotland, was last seen at 11pm on Sunday, May 10.
It is believed he may have travelled to Doncaster and officers are urging anyone who may have seen him to get in touch.
They suspect he may be sleeping rough.
Mr Moverley is 5ft 8in, slim and has dark brown hair with a pony tail.
He speaks with an English accent and was last seen wearing jeans, a white T-shirt and may possibly be wearing a black hooded waterproof jacket.
Mr Moverley needs glasses to see and also has problems with his balance, so may appear intoxicated.
Anyone with information should call Police Scotland on 101.