The two men have never met, but both have said they want to try to mend battered US-Russia ties, which fell to their lowest level since the Cold War after Moscow's 2014 annexation of Ukraine's Crimea.
Earlier it was reported that the White House investigated Flynn’s contacts with Russia. Trump's adviser could discuss sanctions’ lifting with Russian ambassador as a private person, which is forbidden by American law.
When asked about it on Monday, Kremlin spokesman Dmitry Peskov told at a conference call with reporters that Flynn and Kislyak had not discussed lifting sanctions on Moscow.
Asked if there had been talks between any Russian and U.S. representatives on easing sanctions, Peskov said: "We have already said there have not been any (such talks)".