George Rodgers, aged 84, left his home in Ecclesfield, at around 4pm on Tuesday and has not been seen or heard from since.
He left his home intending to walk to a local park but failed to return home.
Mr Rodgers, a father-of-three, who used to work in accounts for British Steel, left home carrying a framed photograph of former player Jimmy Hagan.
He is white, with thin white hair, around 5ft 6 ins tall, and of a medium build.
He was last seen wearing blue jeans and a blue long-sleeved polo shirt.
Anyone with information should call South Yorkshire Police on 101.