The weather department said the cyclonic storm may move west-northwestwards initially.
A fresh low pressure area formed over the Bay of Bengal intensified into a depression on Tuesday, the Meteorological Centre said.
It is likely to further intensify into a cyclonic storm on Wednesday, the MeT Centre said.
"The depression lay centred over east-central and adjoining south-eastern Bay of Bengal and north Andaman Sea, about 950 km south-southeast of Paradip in Odisha," Director of Bhubaneswar MeT Centre, HR Biswas said.
It is likely to intensify into a deep depression shortly and then into a cyclonic storm on Wednesday, Mr Biswas said.
"The cyclonic storm may move west-northwestwards initially and then north-northwestwards, towards Odisha-West Bengal coasts," he said.
The likelihood of a cyclonic storm over Odisha comes barely six months after the cyclone Fani devastated coastal areas of the state on May 3, claiming around 64 lives and leaving many without a shelter.
The warning comes a fortnight after six people were killed in rain that battered the state under the impact of a low pressure area.
Under the impact of the fresh depression, several parts of coastal Odisha are expected to receive rain from November 8 which is likely to intensify, the MeT Centre said.
"We are constantly monitoring the movement and direction of the depression. At present, a clear picture about its possible impact is yet to emerge," a MeT official said.
As sea conditions will be rough and there will be high velocity winds, fishermen have been advised not to venture into deep seas till further notice.