Ms Deepa and Mr Deepak said they were the legal heirs to Jayalalithaa and rightful inheritors of their aunt's plush Poes Garden residence in the heart of the city.
Ms Deepa said she would take legal action against converting the residence into a memorial.
Separately, Mr Deepak, in a letter to Mr Palaniswami, said converting the residence into a memorial should be done only by following the legal process. He said the house belonged to him and his sister.
On Thursday, the Chief Minister announced a judicial probe into Jayalalithaa's death in December and said the house where she lived for years would be converted into a memorial which would be open to the public.