Former councillor Victor Boyhan has said Dun Laoghaire Rathdown County Council needs to resolve the issue if it is to secure the park's future.
Mr Boyhan was last week given a memo which confirmed the council did not have full title to all the park's lands, which lie between Booterstown and Blackrock Dart stations.
A masterplan for the redevelopment of the parklands is currently being considered by the council, but Mr Boyhan said full ownership has to be acquired before it can proceed.
The council has confirmed that freehold for one third of the park's plots are owned by Pembroke Estates Management Ltd.
Of the three plots owned by the company, one is the main Blackrock Park, while the other two are part of larger parklands running along the seafront.
The company acquired the lands in 1870, when plots were bought from local landowners.
As well as freehold title on six plots, the council has a lease on the seventh until 2091. Its lease on the eighth plot expired in 1943.
The council admitted to Mr Boyhan that expert legal opinion was needed to "clarify the options" on the three plots outside its control. Mr Boyhan said the council now needs to pursue full title to the lands to avoid a recurrence of "the Dartmouth Square situation", in which businessman Noel O'Gara bought that two-acre square in Ranelagh for less than €10,000 in 2005.
In June, Dublin City Council offered to buy the square from Mr O'Gara for €300,000, but he rejected this as "an insult".
Since purchasing the land, Mr O'Gara has had several injunctions brought against him to stop him operating a car park and tile shop at the square.
The city council has since decided it will not be attempting to acquire the square by CPO, saying this would prove too expensive.
Pembroke Estates Management is controlled by estate agents Finnegan Menton. Director Iain Finnegan said there has been no approach from Dun Laoghaire-Rathdown County Council to purchase their plots.