The talks took place just as then-president Barack Obama was ordering new actions against Russia over its alleged interference in the US election.
The Washington Post, which first reported the talks, said some senior US officials interpreted Flynn's communications with Russian Ambassador Sergey Kislyak as an inappropriate and possible illegal signal to the Kremlin that it could expect a reprieve from sanctions.
The Post cited unnamed current and former officials familiar with reports by US intelligence and law enforcement agencies that routinely monitor the communications of Russian diplomats.
The Post's sources said Flynn made explicit references to the election-related sanctions, and two sources said that he urged Russia not to overreact to Obama's move, making clear that the two sides would be in a position to review the matter after Trump was sworn in as president.
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The New York Times published a similar account of Flynn's discussions with Kislyak, also citing current and former US officials.
Flynn and Vice President Mike Pence both have denied that the calls with Kislyak involved US sanctions on Russia.
A US law, the Logan Act, forbids private citizens from negotiating state affairs with foreign governments. But no one has ever been prosecuted under the act.
Flynn told the Post in an interview Wednesday that no mention of sanctions was made in his communications with Kislyak.
Yesterday, however, a spokesman for Flynn told the Post and the Times that "while he had no recollection of discussing sanctions, he couldn't be certain that the topic never came up."
The retired three-star general was fired as head of the Defense Intelligence Agency after two years for alleged poor management. He sees militant Islam as the biggest threat to global stability, and has said that Washington and Moscow need to cooperate on the issue.