Director of Area Cyclone Warning Centre, S Balachandran said the system was likely to turn into a depression in the next 24 hours.
"Around December 6 (Wednesday), it is likely to move northwestwards towards north Tamil Nadu and south Andhra Pradesh coasts," he told reporters here.
During the next 24 hours, isolated rainfall was likely in Tamil Nadu and Puducherry, he said, and advised fishermen not to venture into "deep" parts of southern Bay of Bengal for fishing.
During the last 24 hours ended 8.30am today, there were isolated rains in one or two places in Tamil Nadu and Puducherry, he said.
Aranmanaiputhur in Theni district in the state recorded the highest of 6 cm of rainfall during this period, he added.
The "very severe cyclonic storm Ockhi" over east central and adjoining southeast Arabian Sea moved further northwards and lay centred at 5.30am today over east central Arabian Sea near, about 590 km north north west of Amini Divi, 690 km south south west of Mumbai and 870 km south-southwest of Surat.
Ockhi cyclone, which crippled life in Kanyakumari district in Tamil Nadu, and parts of neighbouring Kerala, was "very likely to move north-northeastwards, weaken gradually and cross south Gujarat and adjoining north Maharashtra coasts near Surat as a deep depression by mid night" of December 5 (tomorrow), the Indian Meteorological Department (IMD) said.
Meanwhile, Tamil Nadu government officials said the process of assessing the damage in Kanyakumari was on and that a report will be sent to the Centre later.
On Friday, state Chief Minister K Palaniswami told Prime Minister Narendra Modi during a telephone conversation that the state would soon send a request to Centre seeking financial assistance post-Ockhi damage in the district.
Kanyakumari was battered by Ockhi, damaging standing plantation crops and power infrastructure even as people were rescued from flooded localities last week.
Defence Minister Nirmala Sitharaman had yesterday said a total of 357 fishermen, including 71 from Tamil Nadu, stranded in sea due to cyclone Ockhi, were rescued.
Earlier today, Palaniswami reviewed the rescue and rehabilitation work in Kanyakumari with senior IAS officials.