The square, located in the heart of Dublin 6, is being sold at the December 4th auction with a reserve not to exceed €140,000.
A source revealed to The Irish Times recently that the council were planning to bid for the square but no official would go on the record on the matter.
A number of residents in the area are also rumoured to be preparing a bid.
Dartmouth Square is being sold on the instructions of the court-appointed liquidator of Marble and Granite Tiles.
If the council is successful in acquiring the square it will be second-time lucky.
In 2006 it initiated a compulsory purchase order (CPO) in an effort to bring it into public ownership.
The plan was abandoned after two years amid fears that a legal action by its owner, Athlone businessman Dermot O’Gara, could have exposed it to a legal challenge leading to a “substantial” award.
In 2005 Mr O’Gara achieved notoriety after he bought the park for about €10,000 from PJ Darley, whose ancestors had built the square in the 1880s.
He attempted to operate a tile showroom and car park on the site but his efforts were blocked and the square subsequently returned to public use.
While officials in Dublin City Council are conscious that declaring its intentions may drive up the price at the auction, councillors have attempted to warn off potential bidders by insisting that the two-acre site in the heart of a residential Dublin suburb will not be rezoned for development under any circumstances, irrespective of who the final bidder is.
“Dublin City Council will not facilitate any development or rezoning of this land now or in the future,” Labour councillor Dermot Lacey said.
“It is a very important space in Dublin 6 and I cannot imagine any circumstance in which the council would agree to change its current status.”