The union home secretary directed the central ministries and agencies to keep a regular watch and be in touch with the administrations of Andhra Pradesh and Odisha for any help.
The Union government has already deployed nine teams of the National Disaster Response Force (NDRF) in Andhra Pradesh, 12 in West Bengal and one in Odisha.
The Centre has also kept seven more NDRF units for Andhra Pradesh, five units for West Bengal, and 17 units for Odisha on standby while additional teams are also in readiness if required.
The India Meteorological Department (IMD) is also keeping close track of the cyclone 'Asani' and has issued 20 national bulletins so far, updating local administration about the storm and suggesting measures to save lives.
The cyclone would have wind speeds of 75-85 kmph gusting to 95 kmph on the Andhra Pradesh coast and 45-55 kmph gusting to 65 kmph on Odisha coast.
The cyclone is likely to cause heavy rain in the southern part of West Bengal including Kolkata, Howrah, Purba Medinipur, North and South 24 Parganas and Nadia districts between Monday and Thursday, the weather office had said
Earlier, the weather department said the cyclone is likely to reach Bay of Bengal close to Kakinada-Vishakhapatanam coasts by noon of May 11 and then will move along Andhra coast between Kakinada and Vishakhapatanam (Krishna, East and West Godavari and Vishakhapatanam districts).
The weather office said that very high sea conditions were likely to prevail over west-central and adjoining south Bay of Bengal. The IMD also requested the fishermen not to venture into the deep sea and advised the suspension of fishing operations in the Bay of Bengal till further notice.