The low pressure that formed about 1,000 km south of Calcutta on Tuesday, further intensified into a depression on Wednesday.
The system now lies over a huge expanse of the south-west Bay of Bengal.
'The depression continues to gather strength and is likely to intensify further. It now lies about 600 km south-east of Machilipatnam,' said K.K. Chakraborty, acting deputy director-general at the Regional Meteorological Centre in Alipore.
He said there was a possibility that the system would develop into a cyclone.
'As of now, we find the depression moving north-west towards the Tamil Nadu or Andhra Pradesh coasts. But, we are keeping our fingers crossed. We have already alerted the state government,' said Chakraborty.
Met officials said the effect of the depression is likely to be felt in the coastal districts of Bengal by Thursday night. 'The sky over the city and its adjoining areas is likely to turn grey, leading to showers from Friday morning,' an official said.
'There is a possibility that the depression might hit the Andhra coast in the next 24 hours. At the moment, we can't say for sure whether the depression will hit Bengal. But at the same time, we cannot rule out the possibility,' said Chakraborty.
Met officials have been poring over the radar screen and charts for the past week, with heavy rain battering Calcutta and the districts from the night of October 18 till October 23, leading to floods in many areas.
A strict watch is also being kept on the Andaman Sea, the source of many a cyclone over the Bengal and Orissa coasts at this time of the year.