Two eight-storey blocks on Balbutcher Lane will also be knocked down.
Plans are now being drawn up for the demolition of the Plunkett Tower, a 42-metre, 8,500-tonne building, as well as the other two.
The eight storey blocks each contain 48 three-bed, 24 two-bed and 24 one-bed flats.
The Plunkett building has 90 flats, divided into 30 three, two and one-bed units.
Tenders have been invited for the demolition of the blocks at Balbutcher Lane which are scheduled to come down by the end of the year.
The Sillogue Road tower is expected to be torn to the ground early next year.
While controlled explosions have been used in the past, an alternative method may be engaged for the upcoming demolitions. A mechanical excavator could be employed for the scheme.
Last June, a high-reach excavator was used to pulverise two of the eight-storey towers.
The original seven 15-storey blocks were all named after signatories of the 1916 Proclamation. Since the regeneration of the suburb began in the last decade, residents have been given new accommodation in apartments and houses.
Ballymun Regeneration Ltd, the company set up to oversee the revamp, was granted permission for the latest round of demolitions.
However, the company is handing the project over to Dublin City Council as it is being wound up in the coming weeks.
By the time the remaining three towers are knocked down, all seven 15-storey blocks, 19 eight-storey blocks and 10 four-storey blocks of the original flats in Ballymun will be no more.
They have made way for community buildings, commercial properties and thousands of new homes.
Built in the 1960s, the flats were used to accommodate former residents of Dublin's inner city areas.
In 2004, the demolition of the first tower began. The Patrick Pearse block was knocked down by wrecking machinery. The MacDermott and MacDonagh Towers were demolished by controlled implosion, while the Ceannt, Clarke and Connolly towers were demolished by mechanical means as well.