A meeting of EU ambassadors broke up with no agreement on adding the powerful Shiite militia to the list as "a small number of member states" remained opposed, said an EU diplomat speaking on condition of anonymity.
"Ministers will discuss the issue on Monday," said the source, referring to scheduled talks in Brussels between the bloc's 28 foreign ministers.
Unanimity is required to add the Lebanese group to the dozen people and score of groups currently subject to an EU asset freeze - including Palestinian Islamist movement Hamas and Colombia's FARC guerrillas.
Another diplomatic source told AFP that Ireland and Malta were holding out but that Austria appeared to have dropped objections to the push led by Britain, France and the Netherlands. The positions of the Czech Republic, which has changed government, and Slovakia were unclear.
"We are near a consensus," the source said.
Several countries have objected that it is difficult to separate Hezbollah's military and political wing, which is in government. They also fear destabilising politically fragile Lebanon as the Syrian crisis across its border deteriorates.
Concerns over Hezbollah have mounted in Europe since an attack last year on Israeli tourists in Bulgaria which Sofia blamed on Hezbollah.
In March, a Cyprus court sentenced a Hezbollah member to four years behind bars for planning attacks there.
Hezbollah has been on a US terror black list since 1995.
Britain and the Netherlands are the only EU nations to have placed Hezbollah on their own lists of terrorist groups.
Voice of Russia, AFP