The source said the tanker Aqua had been booked to load the crude oil from a port near Tripoli.
AIS live ship tracking data on Reuters showed the ship, which can carry up to 600,000 barrels of oil, was crossing the Ligurian Sea near the Italian port of Genoa.
An Eni spokesman said on Thursday: "Eni is taking measures to lift as much equity oil as possible from the terminal at Mellitah via an oil tanker which will take the oil to Venice and stock it there for safety reasons."
Mellitah is one of the north African country's more expensive grades with an API gravity rating of 42 degrees and sourced from oilfields in west Libya.
News of the transaction comes after an industry source told Reuters on Wednesday that the Italian oil firm was in talks to charter the ship from a western port. [ID:nLDE73C1X6]
An oil trader said Eni's decision to shift the oil from Libya was likely prompted by concerns that the oil in storage could damage infrastructure if hit by a bomb.
EXPORTS RESUME
Oil trade with Africa's third largest producer is slowly resuming after weeks of paralysis as the civil war cut production and firms balked at financial hurdles linked to international sanctions.Rebels fighting to overthrow Muammar Gaddafi said they need to keep exporting oil to preserve what little cash they had and secure supplies for the civilian population.
Trading firm Trafigura said this week it is discussing the export of crude oil from the rebel-held eastern Libyan ports of Benghazi or Tobruk after Vitol exported an oil cargo last week.
Italy takes around one third of Libya's light, easy-to-refine oil but is so far not considering importing crude oil being produced by Libyan rebels due to restrictions imposed by international sanctions, the foreign ministry said on Wednesday.
Italian firm Eni was one of the country's top producers before the civil war began, with a near 10 percent share of total output of 1.6 million barrels per day.
Its assets in west Libya include the Wafa and Elephant fields and the Bouri offshore terminal, from which an Eni cargo was shipped in mid-March, according to trade and shipping sources.