US President Barack Obama didn't know about State Department's move to ask Bulgaria and Greece to deny overflight permissions to Syria-bound Russian planes, Bloomberg says.

A piece on BloombergView reads that "there's disagreement inside the US government" on how to act to prevent Russian from flying combat missions a new air base inside Syria.

Options discussed include to either "confront Russia inside Syria" or "cooperate" on the fight against the Islamic State (IS) group.

Mentioning Bulgaria and Greece, the text refers to the events of earlier this week when Sofia refused to give clearance to a convoy of Russian military transport planes which Moscow says were carrying humanitarian aid to Syria, but Sofia insists might have been loaded with weapons.

"The [United States] president didn't know about these moves in advance, two officials said, and when he found out, he was upset with the department for not having a more complete and vetted process to respond to the crisis," the author notes.

Earlier, a former CIA official told CBS that the US had asked Bulgaria not to give permission as part of its strategy to address the Russian military's growing presence in Syria.