"Discussions are continuing," about extending the list but "the decision has been put back to the next meeting of foreign ministers" in Brussels on Monday, said a diplomat who asked not to be named.
"It needs to be discussed at a ministerial level," another diplomat said.
Tightening the screws on the Assad regime, the EU last week issued an arms embargo as well as a visa ban and assets freeze against the president's brother, four of his cousins, and others in his inner circle.
EU foreign policy chief Catherine Ashton had warned Assad he could be next.
In a statement, she had said EU sanctions aimed to achieve an immediate change of policy, ending the cycle of violence and swiftly introducing "genuine and comprehensive political reform".
"Failing that, the EU will consider extending the restrictive measures in light of the developments, including at the highest level of leadership," she said.
The talks took place as the UN Security Council moves closer to a resolution to condemn Syria's violent repression of political protests, French Foreign Minister Alain Juppe said Tuesday.
US Secretary of State Hillary Clinton said in Washington that additional steps would be taken "in the days ahead."
Britain and France have lobbied intensively for Assad to be specifically targeted by sanctions after two months of unprecedented protests in which more than 850 people have died and at least 8,000 have been arrested, according to rights groups.
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