She said in a letter to Modi to give the necessary instructions to the ministries of housing and urban poverty alleviation and rural development.
Jayalalithaa requested him to sanction Rs.5,000 crore to construct 50,000 multi-storied tenements to house the flood affected families.
She said the state would provide land for the houses.
Jayalalithaa also said many people living in the slums had also suffered extensive damage but do not have to be relocated.
She asked Modi to make a special allocation of Rs.750 crore for 50,000 houses at the rate of Rs.1.5 lakh per house as central grant.
The chief minister said her government would contribute Rs.1 lakh for in situ reconstruction of flood damaged houses in slums.
Saying one lakh huts were damaged in rains and floods in Tiruvallur, Cuddalore, Kanchipuram and Tuticorin districts, Jayalalithaa also asked Modi for a special allocation of 1 lakh houses additionally.
This would be over and above the normal allocation for the state, under the Indira Awaas Yojana.
She said the allocation should be made at an enhanced unit cost of Rs 1.5 lakh to enable the construction of permanent houses.
On November 23, Jayalalithaa sent a memorandum to Modi asking for central funding of Rs.8,481 crore towards flood relief and an immediate relief of Rs.2,000 crore.
Subsequently, a central government team surveyed the flood destruction.
Even after the team's visit, heavy rains - the worst in a century - battered Chennai and Kanchipuram, Cuddalore and Thiruvallur, resulting in unprecedented floods.
The rains and floods killed 347 people since October 1, and 17.64 lakh people were rescued and housed in relief centres.
During Modi's visit here, he announced a relief of Rs.1,000 crore in addition to the earlier Rs.940 crore.
According to Jayalalithaa, the Rs.940 crore included Rs.133.79 crore of arrears from 2014-15 towards the State Disaster Response Fund (SDRF) and Rs.254.62 crore towards the second instalment of SDRF for current fiscal.