ABC News has not independently confirmed the report, which cites U.S. officials. Reached by ABC News, special counsel spokesman Peter Carr offered no comment.
In response to the story, a spokesman for Trump's attorney Marc Kasowitz issued a statement addressing only what he referred to as a "leak" from the FBI.
"The FBI leak of information regarding the president is outrageous, inexcusable and illegal," the statement read.
The special counsel does not operate under the purview of the FBI but took over the investigation previously led by the agency.
"I don't think it's for me to say whether the conversation I had with the president was an effort to obstruct," Comey said. "I took it as a very disturbing thing, very concerning, but that's a conclusion I'm sure the special counsel will work towards, to try and understand what the intention was there and whether that's an offense."
Trump denies that he asked Comey to drop the Flynn probe — part of his version of the events involving Comey that he said last week he would be "100 percent" willing to recount under oath.
Trump has been emphatic in denying any connection to the 2016 election meddling that the U.S. intelligence community says Russia was behind.
When Comey's dismissal was announced last month, Trump said that he was assured on three occasions by Comey that he was not personally under investigation. In testimony before the Senate Intelligence Committee last week, Comey affirmed that he previously told Trump he was not personally being investigated in the FBI's counterintelligence probe.
Scrutiny of Trump's response to the Russia probe and his interactions with his FBI director would mark a new phase in the investigation.
The investigation into obstruction of justice "began days after Comey was fired on May 9," The Washington Post story notes.
Rosenstein told the Senate Appropriations Committee on Tuesday that Mueller would have "the full degree of independence that he needs to conduct that investigation appropriately" and that he would not follow an order to fire the special counsel "unless I believe those are lawful and appropriate orders."