In his testimony on June 8, Comey told the Senate Intelligence Committee that he believed Trump had fired him over his role as lead of the FBI investigation into Russian interference in the US election and Trump campaign associates' possible ties to Russia.
It quoted five people briefed on the requests and said those who have agreed to be interviewed are Daniel Coats, the director of national intelligence, Admiral Mike Rogers, head of the National Security Agency, and his recently departed deputy, Richard Ledgett.
President Trump on Thursday criticized reports that he is now under investigation for obstruction of justice in connection with the firing of FBI Director James Comey, denouncing it as another "witch hunt" that is unfairly targeting him.
The Post wrote that it based its revelations on interviews with numerous individuals familiar with the investigation, but who spoke on condition of anonymity because none were officially authorized to speak publicly about the Russian Federation probe.
A source familiar with the Mueller investigation confirmed the Post report, saying an examination of possible obstruction of justice charges was "unavoidable" given Comey's testimony, although the issue may not become the main focus of the probe.
"The FBI leak of information regarding the President is outrageous, inexcusable and illegal", a Kasowitz spokesman said. "It wouldn't matter to me what anybody said".
However, when pressed for comment, both the White House and the Senate Intelligence Committee seemed to think that the idea was ridiculous.
"Did the president at any time ask you to stop the FBI investigation into Russian involvement in the 2016 elections?"
"Director Mueller is going to have the full degree of independence that he needs to conduct that investigation appropriately", Rosenstein said.
The news comes one day after Rosenstein affirmed his support for the special counsel, despite recent reports that Trump was weighing Mueller's dismissal.
It is not clear, however, if they will disclose all details of their conversation with Trump or be ordered by the White House to invoke executive privilege.
Before the sacking, Mr Trump had sought and received assurances from Mr Comey that he personally was not under investigation.
Why would Trump consider firing Mueller? . He interviewed the day before, a few days before he was appointed special counsel with the president, who was looking at him potentially to become the next Federal Bureau of Investigation director.
He assured lawmakers Tuesday that he would follow the regulation concerning the special counsel, which says that Mueller can only be fired for good cause.