One diplomatic official told CNN that the Trump administration wants the meeting in Washington, but Moscow has insisted on neutral ground. The official added that Vienna is the likely location.
No official announcements have been made.
Kremlin spokesperson Dmitry Peskov said Thursday that White House national security adviser John Bolton plans to visit Moscow. The National Security Council confirmed later Thursday that Bolton is scheduled to travel to Moscow later this month to discuss the potential meeting.
"As far as we know, such a trip will take place," Peskov said. "So far that's all we can say."
A spokesman for the National Security Council declined to comment on the President's plans for the potential meeting.
CNN reported last week that Moscow and Washington are "exploring" the possibility of a meeting between the two leaders and that Bolton has taken the reins when it comes to dealing with Moscow.
Speaking in London, NATO Secretary General Jens Stoltenberg welcomed the potential meeting, calling dialogue between the two leaders "important" and adding that a meeting "is not in any way contradicting NATO policies."
"NATO is in favor of dialogue, and if you want dialogue, you have to speak to the political leaders," Stoltenberg said.
Trump and Putin have met twice before on the sidelines of global summits and the Russian President said earlier this month that he "regularly" talks with Trump over the phone.
Since Trump assumed the presidency, the two leaders have spoken on the phone eight times, according to White House readouts of the calls.
The relationship Trump has with his Russian counterpart has been under increased scrutiny as special counsel Robert Mueller investigates any potential ties between Russia and Trump campaign associates.
The US leader has praised Putin, suggested that Russia be reinstated to the G7 and has downplayed Russia meddling in the 2016 election.
In March, after pressure from Congress, Trump's administration enacted new sanctions against Russia for its election interference, including the individuals and entities mentioned in indictments from Mueller's investigation.