Cyprus is giving the militants temporary sanctuary
Under a deal brokered last week, the group was flown out of the Middle East in return for Israel lifting the siege and withdrawing from the town.
But their current location is temporary and no final destination has yet been agreed.
The militants are expected to leave in the first half of the week, but ministers still have to agree where they should go.
The BBC's Tim Franks in Brussels says the affair has been a huge diplomatic bungle - initially the plan was for Italy to take them all but no-one told the Italian Government.
'Undertakings'
The militants, described by Israel as "senior terrorists", were confined to the Flamingo hotel in the Cypriot resort of Larnaca after the government agreed to give them temporary sanctuary.
Hotel manager Antonis Josifides told the BBC the 13 were taking meals separately from the rest of the guests and had caused no inconvenience.
It seems Italy may still may take some of the men, along possibly with Spain, Greece, Luxembourg and Canada.
Exiling all of them to the same destination is reported to have now been ruled out for security reasons.
Wherever the deportees end up it will be odd territory, our correspondent says.
As British Foreign Secretary Jack Straw has said, these men have left the Middle East voluntarily and given "undertakings" about good behaviour.
Another British diplomat told the BBC there was nothing to stop them spending a summer on the Italian Riviera and then getting the next flight back to the Middle East.
No country can detain the men against their will unless they put them through some sort of judicial process.
However, Israeli Foreign Minister Shimon Peres said on Friday that Israel reserved the right to demand their extradition - one of the issues which ministers will discuss at the meeting.