The storm lay centred around 98 kilometres east-northeast of Paradeep and 137 kilometres south-southwest of Sagar Island in West Bengal this morning.
The system has been moving nearly northwards with a speed of 15 kilometres per hour during the past six hours.
The Met Department said the storm is very likely to weaken gradually and cross West Bengal and Bangladesh by midnight today.
In Odisha, Met Department warned heavy rain in the districts of Kedrapada, Jagatasingpur, Bhadrak and Balasore districts during the next six hours.
Over 2,000 people in different parts of Jagatsinghpur and Balasore districts were evacuated to safer places as a precautionary measure by the state Government.
The West Bengal Government is working on war footing to minimize the impact of super cyclonic storm Bulbul which is likely to hit the state tonight.