The boat, IFB Rabah, with 14 fishermen on board, had set off from Beypore in Kozhikode district of Kerala Sunday evening.
The boats owner Jaffer said in Kozhikode that he had received information that three of them died in the mishap.
Seven of the fishermen are from Tamil Nadu and the remaining from West Bengal and Odisha.
Two fishermen have been saved from the sea, the Indian Coast Guard said.
''In a swift sea-air #SAR operation @IndiaCoastGuard deployed 03 #ICG ships & aircraft to search for 14 fishermen of IFB Rabah approx 43 NM west #NewMangalore #today. 02 crew found, search for other crew in progress,'' it tweeted.
It is learnt that a ship from Singapore, MV APL Le Havre, had collided with the boat.
The Coast Guard said three of its vessels and choppers are continuing the search for the missing fishermen.