The closure of Poolbeg's oil- burning plant, which produces the vapour, was part of a deal to create more competition in the electricity generation market.
In 2007, the ESB agreed with the energy regulator to reduce its production by 1,300 megawatts.
The chimneys have been one of the most recognisable landmarks in the capital for decades, featuring in films and photographs.
Now, the way has been paved for the demolition of the candy-striped towers as ESB chiefs seek full value for the land.
However, a spokeswoman for the energy company insisted it has yet to make a decision about the chimneys.
"The ESB will be talking to Dublin City Council about (the future of the site) but no decision has been made at the moment," she told the Herald.
She said many people believe the plant is emitting smoke but, in actual fact, it is vapour.
"(The plant) had come to the end of its technical and economic life. In addition to this, there was an agreement with the energy regulator," the spokeswoman said.
However, power will continue to be generated at Poolbeg through its gas-fired station.
Labour's Dermot Lacey, who had unsuccessfully sought the inclusion of the chimneys in the Record of Protected Structures (RPS), said the towers "have become a real icon or backdrop to Dublin Bay".
"They have featured in many a painting, photograph, promotional video and film and should be protected. Perhaps they should now be painted in the Dublin colours, as in that famous Guinness ad," the city councillor said.
He added: "Let's have a public competition for ideas - perhaps the Herald could run this.
"We have been very bad at protecting the industrial heritage in Dublin and perhaps these could be the focal point for such a museum."
Speaking in advance of the closure, Chris Raythorn, a worker at the plant, said there was an "awful lot of people very sad" at the closure.
"They have been here a long time -- 40 years," Mr Raythorn added.
If the chimneys had been added to the RPS, they could not have been demolished.
However, it is understood the prohibitive cost of maintaining the structures means they will more than likely be knocked down.