The Washington Post reported on Wednesday that it interviewed five people briefed on the matter, but it did not identify its sources by name.
A representative for Trump’s lawyer promptly reacted to the allegation.
"The FBI leak of information regarding the President is outrageous, inexcusable and illegal," Mark Corallo, spokesperson for Trump's lawyer Marc Kasowitz, said.
The special counsel launched its investigation of Trump just days after Trump fired former FBI director James Comey on May 9, the report said.
Obstruction of justice is an impeachable offense.
Russia has repeatedly denied allegations that it interfered in the US election, insisting that it does not meddle in the affairs of other countries.