Meteorologists said it would move further in the same direction and is likely to cross the coast of India's Andhra Pradesh by Friday or Saturday.
"It's unlikely to make landfall," Indian newspaper 'The Hindu' quoted saying M Mohapatra, the chief of the country's Cyclone Warning Division.
The Bangladesh met office had said earlier that chances of Kyant making landfall in Bangladesh coast was very less.
Its latest weather bulletin says that the cyclonic storm has weakened into deep depression and moved southwestwards.
All maritime ports in Bangladesh have been advised to lower the 'distant warning signal number two' and hoist 'distant cautionary signal number one.'
Maximum sustained wind speed within 48 kms of the centre is about 50 kmph rising to 60 kmph in gusts.
The met office asks all fishing boats over north Bay to remain close to the coast and proceed with caution till further notice.
The met office forecasts rain and thunder showers with gusty winds over Dhaka, Mymensingh, Khulna, Barisal, Chittagong and Sylhet divisions and weather may remain mainly dry with partly cloudy sky elsewhere over the country.
It said the temperature in daytime may fall by one or two degree Celsius.