Vladimir Putin has discussed working with international "partners" to take on Islamic State militants, according to Russian media.
The Russian president was reported to have talked about the issue with his Security Council today.
Kremlin spokesman Dmitry Peskov would not say which countries Russia may be willing to work with.
Any US air strikes against Islamic State militants in Syria without a UN Security Council mandate would be a "gross violation of international law", Russia has warned.
President Obama said the US could strike targets in Syria as well as Iraq, saying he would "hunt down terrorists who threaten our country wherever they are."
But Russia claimed any move without the consent of the UN would be an "act of aggression".
"The US president has spoken directly about the possibility of strikes by the US armed forces against IS positions in Syria without the consent of the legitimate government," foreign ministry spokesman Alexander Lukashevich said.
"This step, in the absence of a UN Security Council decision, would be an act of aggression, a gross violation of international law."
Did Philip Hammond misspeak or did he reveal the thinking at the highest levels of government on military action in Syria?
President Obama - a leader who thought his legacy would be ending two conflicts - has plunged the US into the maelstrom of two civil wars.
A social media campaign imitating the popular Ice Bucket Challenge has gone viral. Its target is Islamic State.