Mueller's office has reached out to Director of National Intelligence Daniel Coats, National Security Agency Director Adm. Mike Rogers and recently retired deputy NSA director Richard Ledgett. Senate Intelligence Committee Vice Chairman Sen.
Mueller has also gathered the memos which Comey created following the now-infamous meeting in which he claims Trump asked him to end his investigation into Flynn.
Mark Corallo, a spokesman for Trump's private attorney, Marc Kasowitz, immediately condemned the Post report.
He called the leak "outrageous, inexcusable and illegal" - but he did not deny the story.
Trump lashed out on Twitter early on Thursday. A spokesman declined to comment when asked by the Post.
According to the Post and Wall Street Journal reports, Ledgett wrote a memo describing a phone call Trump made to Coats in which the president asked Coats to publicly say his campaign did not collude with Russian Federation.
Deputy attorney general Rod Rosenstein, who appointed Mr Mueller last month, testified Tuesday he has seen no evidence of good cause to fire Mr Mueller.
Mr Mueller is also alleged to be looking for any evidence of possible financial crimes among Trump associates, officials added.
Comey was later sacked, with Trump acknowledging that the Russian investigation was on his mind when he made a decision to dismiss him.
Mueller met with Sens.
They say senior intelligence officials will be interviewed about whether Mr Trump tried to end an inquiry into his sacked national security adviser.
Significantly, Preet Bharara, the India-born former top United States federal prosecutor, earlier this week had said that there was enough evidence to begin an obstruction of justice case against Trump over his alleged interference in the Russian Federation probe.
An obstruction of justice finding could form the basis for Mr Trump's impeachment but such a step would face a steep hurdle because it would require approval by the US House of Representatives, which is controlled by the President's fellow Republicans. "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".
Obstruction of justice is essentially defined as intentionally intervening or tampering with an ongoing investigation. However, the key to proving obstruction of justice is that the intervention was done for corrupt purposes.