The children died following a fire in 1916 during a fundraising performance at the Garrick Theatre.
Although there is a commemorative plaque close to the site of the tragedy, residents say they would like a "lasting memorial".
Relatives said the tragedy was "part of living history".
Andrew Rutherford, whose great aunt Nellie died aged 13, said: "She was spoken of by the family over many years.
"The story I heard was that several girls were doing a show on stage among candlelight.
"It's very important these things are still remembered."
Former Hereford Times news editor Nigel Heins said more than 40 children were involved in the amateur show, including the girls, whose costumes were made of cotton wool.
At the end of the first performance, a fire broke out and the girls' costumes were soon alight.
Six children died that night from their burns - another two later died in hospital.  The theatre has since been demolished.
Mr Heins said: "I think something that awful should never be forgotten."
Herefordshire councillor Mark Hubbard said he hoped to bring the idea of a memorial before the council shortly.
"I think it's a fascinating story that connects people with their community," he said.
"We could do something really nice as a lasting memorial to those eight little girls."
Mr Hubbard called on relatives of the children and supporters of the idea to contact him.
Hear how the fire at Garrick House broke out and find out more about the story..
A memorial to commemorate a wartime tragedy that killed eight young girls should be erected in Hereford, residents have said.