The city's public art manager will now examine other funding proposals, such as staging an annual concert.
According to a report presented to councillors this week, direct council funding is now firmly off the table.
"The public art manager reported that, while there is no doubt that Luke Kelly was a significant figure in the history of Irish music and that the proposal [to commission a statue] qualified in regard to the condition that the subject has been dead for at least 20 years, there was no funding available," the report states.
"The arts manager proposed an annual concert focussing on singing ... to raise funds for music bursaries for residents in the north inner city docklands area and potentially to raise funding for the statue."
A raft of proposals to ensure the construction of a statue has been put forward.
The Dublin Docklands Development Authority (DDDA) originally commissioned the statue in 2005 after being contacted by council bosses.
However the DDDA told the Kelly family in 2009 it was shelving plans as it couldn't afford it.
DDDA documents state: "The budget was estimated to be €80,000 to be funded on an equal basis by the authority and Dublin City Council."
In 2010, Independent councillor Christy Burke revealed that he had contacted Bono and others to try to fund a statue.
"The people of Dublin want this and, without doubt, Luke deserves it. It's about time we deliver on this promise that was made to the Kelly family years ago," he told the Herald.