"I was contacted by a guy in England who brought it to my attention," Mr O'Callaghan told the Herald. "It is something worth getting back."
Mr O'Callaghan had wanted the banner returned to mark the centenary celebrations of Na Fianna Eireann last year.
His hopes were dashed, but he said it still should be displayed in City Hall for a period of time.
"It does not serve much purpose in the Imperial War Museum. It's in the Home Countries section there," he said.
Mr O'Callaghan has tabled a motion for tonight's council meeting requesting Mr Tierney write to the director of collections at the museum to have the item loaned to the council.
Na Fianna Eireann, which was the republican youth movement, was founded on August 16, 1909, in a hall on Dublin's Camden Street.
A committee that included Constance Markievicz and Bulmer Hobson called the meeting to recruit boys to a new nationalist body.
Many historians view the so-called boy's army as playing a crucial role in the 1916 Rising.
Mr O'Callaghan said the banner "is something that belongs in Dublin".
Na Fianna Eireann was similar to the boy scouts movement, though it differed in that members were trained in shooting.
Its proclamation in 1914 stated it was the organisation's aim "to train the boys of Ireland to fight Ireland's battle when they are men".
Na Fianna continued for decades and by the 1980s girls as well as boys were admitted to its ranks.
However, with the development of Sinn Fein Youth, Fianna Eireann was disbanded and Ogra Shinn Fein took its place.