Met department issued a warning to both the states saying they may experience heavy rains for the next two days.
A deep depression in the Bay of Bengal has intensified further and laid centred 170 kilometres off Chennai coast. It is likely to move north-northeastwards and intensify into a deep depression during next 24 hours and further into a cyclonic storm in the next 48 hours.
Heavy rains are likely at a few places in Tamil Nadu and Kerala too. The Met department has advised the fishermen not to venture into the sea along the Tamil Nadu coast.
Chennai has already recorded 101 mm rainfall since Tuesday.
AP Chief Minister N Chandrababu Naidu has asked all the district collectors to take all necessary steps and evacuate people of low lying areas immediately if necessary.
Chennai is experiencing the heaviest rainfall in May in the last five years, and the heaviest since the 2015 floods.
Rains had also affected the voter turnout during the Assembly elections on Monday in some places in Chennai and South Tamil Nadu.
Kerala, too, is witnessing heavy rains with Ernakulam and some southern districts of the state receiving heavy downpour