Among those evacuated to neighboring countries Iraq and Lebanon are high-ranking commanders of Iran's Quds Force, the external branch of the Iranian Revolutionary Guard, according to the newspaper's unnamed sources.
Security personnel, as well as some diplomatic staff and their families, and civilians are also being evacuated, the sources say, including two from the Revolutionary Guard. The evacuations are reported to have begun on Friday morning. They are taking place from both the Iranian embassy in Damascus and military bases belonging to the Revolutionary Guard.
Fighting jihadists have rapidly advanced south towards Syria's third-largest city Homs, after previously taking control of the country's fourth-largest city Hama and second-largest city Aleppo.
If the militant Islamists take control of Homs, the capital Damascus will be cut off from President Bashar al-Assad's main strongholds on the coast.
Besides Russia, Iran and Shia militias backed by Tehran have been the Syrian regime's closest allies during the civil war.
Iran announced late on Friday that it supports its close ally al-Assad and the Syrian government forces. Iranian Foreign Minister Abbas Araghchi then said that Tehran supports Damascus "with whatever they need".