"We received the request on Saturday and are examining it," the official said on condition of anonymity.
Washington is concerned that Moscow could be increasing its military support to the regime of President Bashar al-Assad, an issue raised by US Secretary of State John Kerry to his Russian counterpart Sergei Lavrov over the weekend.
The New York Times has reported that Russia has sent a military advance team to Syria and was taking other steps that Washington fears may signal plans to vastly expand its military support for President Bashar al-Assad.
Russia has asked Greece to permit the passage of two planes between September 1 and 24, the Greek official said. Moscow has dismissed American concerns, saying its aid to al-Assad is nothing extraordinary.
"The Russian side has never concealed the fact that it is sending military equipment to the Syrian authorities to help them fight terrorism," Russian foreign ministry spokeswoman Maria Zakharova told AFP earlier today, commenting on the Kerry-Lavrov phone talks.