The senator and other members of Congress are now in Moscow meeting with government officials.
The information could not be immediately confirmed by us officials.
Senator Paul recently defended the president's meeting, citing overlapping interests for both countries.
The summit drew sharp criticism at home after Trump suggested he was inclined to believe Putin's version of events regarding the 2016 USA presidential election - that is, Russia's denial of meddling - over the conclusions of the United States intelligence community.
Special Counsel Robert Mueller is investigating Russian meddling in the 2016 presidential campaign, after the U.S. intelligence community concluded that Putin ordered efforts to undermine Democratic candidate Hillary Clinton and aid Trump.
Trump has invited Putin to D.C.as well.
"The hatred of the president is so intense that partisans would rather risk war than give diplomacy a chance", Paul said in a long defense of Trump on the Senate floor, days after the summit.
After meeting with Paul for an hour, Kosachev publicly reiterated that Russian Federation was not involved in election meddling.
This week, both Democratic and Republican senators introduced a bill that would impose the harshest sanctions yet on Moscow as punishment for its USA election interference, as well as its activities in Ukraine and Syria.
Mr. Paul's press released noted that nuclear proliferation and terrorism will be among the issues the global leaders discuss.
"We had general discussions about a lot of issues", Paul responded. "The biggest issue right now is no dialogue".
Senior Russian lawmaker Konstantin Kosachev, who was also in the room, reiterated the Russian position that "there was no interference in 2016", adding "there of course will not be any interference in the elections this year".