Putin and Trump first met at a G20 summit in Hamburg in July when they discussed allegations of Russian meddling in the US presidential election, but agreed to focus on better ties rather than litigating the past, Reuters reported.
Relations between Moscow and Washington have soured further since, however.
Trump in August grudgingly signed off on new sanctions against Russia, a move Moscow said ended hopes for better ties. Putin, dismayed by the sanctions, ordered Washington to more than halve its embassy and consular staff in Russia.
But when asked if Putin and Trump might meet at an Asia-Pacific Economic Cooperation (APEC) summit taking place next week in Vietnam, Kremlin spokesman Dmitry Peskov said Moscow did not rule out such a meeting.
"It (the meeting) is indeed being discussed," Peskov told reporters on a conference call.
"It's hard to overestimate the importance and significance for all international matters of any contact between the presidents of Russia and the United States," said Peskov.
The APEC summit is taking place in the Vietnamese city of Danang from Nov. 8-10.