Fuels have become a vital resource in the more than two-month-old war between rebels and forces loyal to leader Muammar Gaddafi. OPEC member Libya is reliant on fuel imports even during peacetime because of insufficient refining capacity.
AIS ship tracking data on Reuters showed it was near Greece early on Monday and heading south toward east Libya but the vessel has not sent a signal since. The Warwick was due on Tuesday the data showed but it was not immediately clear if the tanker had reached its destination.
It typically takes between one and two days to cross the Mediterranean from north to south.
One trade source said that the tanker was booked by trading firm Vitol but this could not be immediately be confirmed.
Trade sources said the group has won the right to deliver around 80,000 tonnes of fuel this month to east Libya in May.