Mueller is investigating Moscow’s efforts to help elect Trump and whether he sought to block the probe into contacts his associates have had with Russians, The Washington Post reported on Monday night.
Trump declared in tweets earlier on Monday that he has the “absolute right” to pardon himself and called Mueller unconstitutional.
As the two sides head toward a confrontation over a presidential interview in the coming weeks, newly hired White House lawyer Emmet Flood and other attorneys are strategising about how to handle a subpoena from Mueller that would seek to compel Trump to testify in the investigation.
Several White House officials said Flood has cautioned Trump and others about the unpredictability of a subpoena fight that could be decided by the Supreme Court.
Trump lawyer Rudolph W. Giuliani told The Washington Post that the outcome of such a showdown is uncertain.
“Both sides are taking a big risk with a subpoena fight,” he said.
Meanwhile, Giuliani and other advisers have begun making plans to prepare Trump for a possible sit-down with Mueller.
Another Trump lawyer, Jane Raskin, talks with Mueller deputy James Quarles at least three times a week.
She is reviewing the classified conversations Trump and other top aides have had with foreign leaders, such as Russian Foreign Minister Sergei Lavrov.
Bill Clinton was the first US President subpoenaed to testify in a criminal probe, before his lawyers negotiated the terms of a voluntary interview instead.