Sputnik news agency cited sources as saying that the diplomatic breakthrough is brokered by Russia and the UAE.
According to the report, the consulate is expected to reopen after Eid al-Fitr, which will be celebrated late in April.
The sources added the reopening will be preceded by a visit by Saudi foreign minister to Damascus to meet President Bashar al-Assad and Syrian officials.
Saudi Arabia closed its embassy in Damascus and withdrew all diplomats in March 2012.
