The militants are waiting to hear about their destination
Spanish state radio had earlier reported that an agreement had been brokered to send the men to seven European states, including Cyprus - which is not in the European Union.
But Cypriot Foreign Minister Ioannis Cassoulides said no final deal had yet been struck.
Temporary guests
Mr Cassoulides expressed optimism about continuing talks about the fate of the Palestinians.
"Things are moving very well and we expect a resolution of this issue in the coming days," he told Reuters news agency.
However, he categorically denied that his country would be offering a permanent refuge to any of the militants.
Mr Cassoulides said that under the current plan, Spain and Italy were each expected to take three of the men; Greece and Ireland to accommodate four between them, and Portugal and Belgium would each accept one.
The Cypriot foreign minister said that Finland late in the day had offered to take the remaining Palestinian, but that final arrangements were still being discussed.
Cyprus accepted the militants as part of a deal to end the siege at the Church of the Nativity in Bethlehem.
But it has said all along that it was a temporary measure until the EU had decided where their ultimate destinations would be.
It is not known when they will be moved to their host countries.
Diplomatic coup
Israel regards the 13 as the most dangerous of the Palestinian militants who barricaded themselves inside the Church of the Nativity for nearly 40 days.
The EU offered to take the militants into exile to end the standoff between the Israeli army and the Palestinians at the church on 10 May. The deal was supported by the United States and the Vatican.
EU foreign ministers have decided that none of the 13 should face arrest, and they have received assurances from Israeli Foreign Minister Shimon Peres that Israel will not seek their extradition.
The men will also be entitled to reunification with their families at a later date.
The resolution of the Bethlehem siege has been seen as a diplomatic coup for the EU, whose interventions in the Middle East have tended to be overshadowed by the United States.
"Without the European Union, the Church of the Nativity would still be under siege today and Israeli troops would still be on the streets of Bethlehem," said Spanish Foreign Minister Josep Pique.