The ESB will decide by the end of this year whether it will knock down the Poolbeg chimneys.
The power station in Poolbeg ceased operation in 2010, and a review of the use of the site is now under way.
According to The Irish Times, the ESB told the Minister for Tourism, Leo Varadkar, that structural and repair works needed to keep the twin chimneys standing may not be the best possible use of resources.
The twin chimneys stand a slightly more than 207 metres, and are visible from a large portion of the city's coastal areas. The power station was completed in 1971.
An application to have the chimney stacks listed as protected structures, put forward by Labour councillor Dermot Lacey, was refused around the time of the station's closure.
"These two chimneys are welcoming signs, and I don't buy the argument that they're going to cost a load of money to keep in repair … all that is needed is painting," said Chairman of the Environment Group of Ringsend, Damien Cassidy.
"They've served the community and the city for the last 40 years, and they are a piece of architectural beauty."