"It is expected that the meeting will take place in early days of next week," the source said.
Earlier this week, director of the Center for Current Policy in Russia Alexey Chesnakov posted on Facebook that Surkov and Volker might meet in Minsk.
The U.S. party proposed a meeting in Vienna, and Russians wanted Kaliningrad, he wrote.
"Minsk could be a convenient meeting point for both sides. It's a good compromise for the Russian delegation - the territory of the Union State of Russia and Belarus, and not far from Kaliningrad. For the Americans, not a bigger deal either, just a few more hours on a plane," Chesnakov wrote.
A career diplomat, Volker is a former aide to Republican Senator John McCain, a Russia hawk who wants the United States to supply lethal weapons to Ukraine, a move the previous administration under Barack Obama shied away from. Volker, a former U.S. ambassador to NATO, was appointed to his current role on July 7 to help resolve the conflict between Ukrainian troops and pro-Russian separatists, which has killed more than 10,000 people since 2014.