Twenty-three people "of African and Arab nationality" were saved by Libyan coastguards, added the source, cited in Tuesday´s edition of the private newspaper Oea.
"Three boats left on Sunday from the Tripoli suburb of Sidi Belal carrying a total of 257 people," the source was quoted as saying. "One of them sank, but we do not know if the others arrived safely at their destination."
It was not known how many people were aboard the boat that went down.
Earlier Egypt´s state news agency MENA reported from Cairo that dozens of people were feared to have drowned.
Ahmed Rizq, responsible for consular affairs at the foreign ministry in Cairo, told the agency that 20 passengers, including six Egyptians, had been saved by Libyan rescue workers.
Rizq said the ship sank some 30 kilometres (20 miles) off Libya.
The Libyan interior ministry source added that elsewhere off the coast on Monday an Italian tanker rescued 350 illegal migrants after they got into difficulties.
At least 40 people drowned after a boat carrying illegal migrants from Libya to Italy capsized in June 2008.
Italy said on Monday it will soon launch joint sea patrols with Libya aimed at stopping the heavy influx of illegal immigrants using Libya as a transit point.
Interior Minister Roberto Maroni said the patrols will begin on May 15, a day he expects to "mark the end" of illegal migration from North Africa.
His comments came a day after more than 460 illegal immigrants were found off the coasts of Sicily and Lampedusa and another 166 around the Sicilian city of Catania.
Italy and Libya signed a deal in August 2008 under which Tripoli committed itself to reinforce the fight against illegal immigration by taking part in joint sea patrols.
Nearly 37,000 illegal immigrants landed on Italian coasts last year, a 75-percent rise from 2007, according to the interior ministry in Rome.
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