On the second day of their informal talks in Italy on Saturday, the ministers are also expected to try and bridge their differences over a new UN resolution on Iraq.
Earlier on Friday, UK Foreign Minister Jack Straw had expressed hope his EU counterparts would agree to ban the non-military wings of Hamas, effectively freezing its funding.
"I think the case against Hamas, its so called political wing as well as its military wing, is now overwhelming," Straw said.
UK and Netherlands have led the call for blacklisting Hamas, but a group including France, Belgium and Greece had opposed the move, saying it would be counterproductive.
Diplomatic sources however said France has dropped those reservations since a new round of violence erupted in the Middle East last month.
"Its no longer a problem," one diplomat said. Diplomats said a decision was likely by the end of the day.