The Post said its sources would not further identify the official, who was described as a senior White House adviser who is close to Mr Trump.
Trump's approval among voters reached a new low for the third time this month, with 41 percent saying they still approve of his job performance and 53 percent disapproving - a 4-point drop in his net approval rating from the previous poll.
The survey was taken between May 14 and May 18, a whirlwind period in which Trump's firing of FBI Director James Comey and reports of the president's disclosure of highly-classified information to Russian officials dominated the news cycle.
Just 22 percent of American voters, by contrast, said they felt Trump's decision to share information with Russian officials was "appropriate" and 39 percent said they are "very" or "somewhat" confident in his ability to handle classified intelligence.
A Reuters/Ipsos poll released Friday indicates only 38 percent of us adults now approve of the president, while 56 percent said they disapprove of his performance.More news: Inflation rate jumps to highest level since September 2013
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Later in the week, the Justice Department appointed former Federal Bureau of Investigation director Robert Mueller to oversee an independent probe into contacts between Russian Federation and the Trump campaign. Gallup's daily tracking poll, for example, set Trump's record low at 35 percent on March 28. Trump explicitly denies that there has been intrigue with Russian Federation and characterizes the ongoing research at the heart of the witch hunt research.
50% said Trump wasn't "able to serve as Commander-in-Chief", and about the same percentage (52%) said they were not confident he could keep the country safe from terrorism.
While Mr Trump remains popular with members of his own party, many rank-and-file Republicans appear to have backed off their support for the President during the past week.
The Reuters poll was conducted online in English across the United States with 1,971 adult respondents, including 721 Republicans and 795 Democrats.