Last Saturday a blue plaque was unveiled at 9 East Parade in the city centre to commemorate Sir Nathaniel Creswick, a “founding father” of the game who worked in the building.
Other influential figures in the development of football lived and worked nearby, said Mr Wood.
“You associate Stratford with Shakespeare, you associate the Cavern Club in Liverpool with The Beatles.
“If you go to the Amazon and talk to the local people, show them a copy of Revolver, Shakespeare’s books and a football, we are quite confident which one most people will recognise.
“Football is bigger than Shakespeare and The Beatles, so therefore 9 East Parade is Sheffield’s Cavern Club.”
The building itself – now a law firm’s offices – would be too small for a museum, Mr Wood said.
“Nearby there are lots of buildings up for lease. There are possibilities in that part of the centre of Sheffield to develop something.
“A museum is still an aspiration for Sheffield because Sheffield, being the birthplace for football, does need somewhere to display things.”
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