Trump is being investigated by special counsel Robert Mueller for possible obstruction of justice, US media reports say.
They say senior intelligence officials will be interviewed about whether Mr Trump tried to end an inquiry into his sacked national security adviser.
Mr Trump's legal team said the latest leak to the media was "outrageous".
Mr Mueller is overseeing an FBI inquiry into Russia's alleged meddling the 2016 US election and any Trump links to it.
President Trump has repeatedly denied any collusion with Russia, describing the ongoing inquiry as a "witch hunt".
On Wednesday, the Washington Post described the decision by Mr Mueller to investigate President Trump's own conduct as a major turning point in the investigation, which until recently focused on the Russian angle.
Quoting unnamed officials, the newspaper said Daniel Coats, the director of national intelligence, Mike Rogers, the head of the National Security Agency, and Richard Ledgett, until recently Mr Rogers' deputy, agreed to be interviewed by investigators.
The questioning could happen as early as this week.
The unnamed officials told the newspaper the obstruction of justice investigation began just days after President Trump fired former FBI director James Comey on 9 May.
Before the sacking, Mr Trump had sought and received assurances from Mr Comey that he personally was not under investigation.
keyboard shortcuts: V vote up article J next comment K previous comment