However, four fishermen were rescued from the boat, they said.
The fishermen had ventured into the waters last night after the state government lifted the one-month long ban on fishing, which is observed every year during the breeding period of fish.
"The Indian Coast Guard received information about the trawler in distress last night. They managed to bring to safety four fishermen while two are missing and feared dead," a police official attached to Vasco Police Station said.
The mishap occurred a few kilometres away from the coast, police said, adding that search for the two fishermen was on.