France and the United Kingdom are expected to argue that the move would increase pressure on Damascus for a political solution.
However, several EU states are totally opposed to ending the arms embargo, which expires on May 31.
EU officials have warned against jeopardising a current initiative to hold an international peace conference.
Syria’s foreign minister confirmed on Sunday that the government would “in principle” attend the conference which the United States and Russia hope will take place in Geneva next month.
Walid Muallem said it would be “a good opportunity for a political solution” to the conflict, which the United Nations says has left more than 80,000 people dead.
Members of the main opposition coalition are currently discussing whether to attend the conference, but spokesmen have said they would if President Bashar al-Assad agreed to step down.
Arriving for the talks in Brussels on Monday, several foreign ministers and EU foreign policy chief Catherine Ashton said it was vital to give the planned Geneva talks a chance.
Luxembourg Foreign Minister Jean Asselborn said first and foremost the EU had to “do everything to support as Europeans the American and Russian initiative.”
UK Foreign Secretary William Hague said that Britain fully backed the Geneva conference as “in the end there is only a political and diplomatically supported solution.”