"We would agree to the departure of Assad and the transfer of his powers to a regime figure, who would lead a transitional period like what happened in Yemen," SNC spokesman George Sabra told AFP.
The Arab League on Monday called on Assad to swiftly step aside in order to end the fighting that has swept across the country.
"There is agreement on the need for the rapid resignation of President Bashar al-Assad," Qatar's Prime Minister Sheikh Hamad bin Khalifa Al-Thani told journalists at the end of a ministerial meeting in Doha.
"We accept this initiative because the priority today is to put an end to the massacres and protect Syrian civilians, not the trial of Assad," Sabra said.
Asked about which regime figure could lead such a transition, Sabra said Syria has patriotic figures both in the regime and among officers in the Syrian army who could take such a role, without giving further details.
Earlier this year, the Arab League urged Assad to transfer power to his deputy and make way for a national unity government, in a plan similar to that accepted by Yemen's president Ali Abdullah Saleh after months of deadly anti-regime protests.
In power since 1978, Saleh stepped down in February and handed over to Vice President Abdrabuh Mansur Hadi under a power transfer deal brokered by Gulf Arab states after months of deadly protests.
But the Syrian regime has rejected all Arab League calls for a transition plan that would see Assad leave power.