A high tide has already begun in Digha, they said.
Fishermen have been alerted and asked not to venture into the sea.
Lakhs of people have been evacuated to safer places.
South Eastern Railway sources said, "In all likelihood, all south-bound trains beyond Kharagpur are likely to be cancelled." Kolkata, however, is expected to experience light to medium rainfall and an overcast sky, the MeT office said.
There would be no direct impact of the cyclone in Kolkata, they said.
Phailin, a "very severe" cyclone, is expected to hit the east coast today evening, with winds gusting up to 220 kmph. Lakhs of people have been evacuated to safer places.